The current official position on Jerusalem and Muhammed in Islam is basically this:
...it was Al-Masjid al-Aqsa in Jerusalem that was the destination of the Prophet, peace and blessings be upon him, on the famous Night Journey referred to in the Qur'an and hadith. It was here that Muhammad led the prophets in prayer and it was from here that he ascended through the heavens visiting the prophets again on his way to the sidrat al-muntaha, the Lote Tree of the Furthest Limit, and his encounter with his Lord.
Initially, Rashidun and Umayyad-era scholars were in disagreement about the location of the "remotest sanctuary" with some arguing it was actually located near Mecca. Eventually scholarly consensus determined that its location was indeed in Jerusalem.[55 - Meri and Bacharach, 2006, p.50]
On the question of Islam's relationship with Jerusalem and Jerusalem in the Koran, there are Sheikh Abdul Hadi Palazzi's opinions:-
The most common argument against Muslim acknowledgment of Israeli sovereignty over Jerusalem is that, since al-Quds [Jerusalem] (4) is a Holy Place for Muslims, Muslims cannot accept that it is ruled by non-Muslims, because such acceptance amounts to a betrayal of Islam.
Before expressing our point of view on this question, we must reflect upon the reason for which Jerusalem and Masjid al-Aqsa [the Al Aksa mosque] hold such a sacred position in Islamic faith.
As is well known, the inclusion of Jerusalem among Islamic holy places derives from al-Mi'raj, the Ascension of the Prophet Muhammed to heaven. The Ascension began at the Rock, usually identified by Muslim scholars as the Foundation Stone of the Jewish Temple in Jerusalem referred to in Jewish sources.
Recalling this link requires us to admit that there is no connection between al-Miraj [the Ascension] and Muslim sovereign rights over Jerusalem since, in the time that al-Miraj took place, the City was not under Islamic, but under Byzantine administration. Moreover, the Qur'an expressly recognizes that Jerusalem plays for Jews the same role that Mecca does for Muslims.
"...They would not follow thy direction of prayer (qiblah), nor art thou to follow their direction of prayer; nor indeed will they follow each other's direction of prayer..." (5)
All Qur'anic commentators explain that "thy qiblah" [direction of prayer for Muslims] is clearly the Ka'bah of Mecca, while "their qiblah" [direction of prayer for Jews] refers to the Temple Mount in Jerusalem.
To quote only one of the most important Muslim commentators, we read in Qadn Baydawn's Commentary:
"Verily, in their prayers Jews orientate themselves toward the Rock (sakhrah), while Christians orientate themselves eastwards..." (6)
In complete opposition to what "Islamic" fundamentalists continuously claim, the Book of Islam [the Qur'an] - as we have just now seen - recognizes Jerusalem as the Jewish direction of prayer.
...from an Islamic point of view - despite opposing, groundless claims - there is no reason for Muslims to deny the State of Israel - which is a JEWISH state - complete sovereignty over Jerusalem.
...The Kotel was effectively, according to the Islamic tradition, the place where al-Buraq [the Prophet's steed] was tethered, but it was already an existing part of the Herodian structure. Muslims have never prayed close to it, and it has never had a special relevance in Islam. On the contrary, everyone knows how important it is for Jewish worshippers.
Apart from Mecca, no Islamic holy place is off-limits for non-Muslims. Historical sources say that the Prophet Muhammad entertained a delegation of Christians from Najran in the Mosque of Medina, and permitted them to celebrate a mass inside the Mosque, notwithstanding the fact that Christian rites can include words that are against Islam [such as stating that Jesus is God].
There is nothing in Jewish worship that can be offensive for Muslims, and nothing in Islamic Law prevents Jews to pray on Haram al-Sharif/Har Habayyit (the Temple Mount), in the Cave of Machpela or in any other place that is regarded as holy by Muslims.
Daniel Pipes quotes the late Moshe Kohn:
Jerusalem and Zion appear as frequently in the Qur'an "as they do in the Hindu Bhagavad-Gita, the Taoist Tao-Te Ching, the Buddhist Dhamapada and the Zoroastrian Zend Avesta"—which is to say, not once.
...the first qibla (direction of prayer) of Islam, did not last long. The Jews criticized the new faith and rejected the friendly Islamic gestures; not long after, the Qur'an broke with them, probably in early 624. The explanation of this change comes in a Qur'anic verse instructing the faithful no longer to pray toward Syria but instead toward Mecca. The passage (2:142-52) begins by anticipating questions about this abrupt change:
The Fools among the people will say: "What has turned them [the Muslims] from the qibla to which they were always used?"
God then provides the answer:
We appointed the qibla that to which you was used, only to test those who followed the Messenger [Muhammad] from those who would turn on their heels [on Islam].
In other words, the new qibla served as a way to distinguish Muslims from Jews. From now on, Mecca would be the direction of prayer:
now shall we turn you to a qibla that shall please you. Then turn your face in the direction of the Sacred Mosque [in Mecca]. Wherever you are, turn your faces in that direction.
The Qur'an then reiterates the point about no longer paying attention to Jews:
Even if you were to bring all the signs to the people of the Book [i.e., Jews], they would not follow your qibla.
and adds more:
...note a passage of the Qur'an (17:1) describing the Prophet Muhammad's Night Journey to heaven (isra'):
Glory to He who took His servant by night from the Sacred Mosque to the furthest mosque. (Subhana allathina asra bi-'abdihi laylatan min al-masjidi al-harami ila al-masjidi al-aqsa.)
When this Qur'anic passage was first revealed, in about 621, a place called the Sacred Mosque already existed in Mecca. In contrast, the "furthest mosque" was a turn of phrase, not a place. Some early Muslims understood it as metaphorical or as a place in heaven. And if the "furthest mosque" did exist on earth, Palestine would seem an unlikely location, for many reasons. Some of them:
Elsewhere in the Qur'an (30:1), Palestine is called "the closest land" (adna al-ard). Palestine had not yet been conquered by the Muslims and contained not a single mosque. The "furthest mosque" was apparently identified with places inside Arabia: either Medina or a town called Ji'rana, about ten miles from Mecca, which the Prophet visited in 630.
The earliest Muslim accounts of Jerusalem, such as the description of Caliph 'Umar's reported visit to the city just after the Muslims conquest in 638, nowhere identify the Temple Mount with the "furthest mosque" of the Qur'an. The Qur'anic inscriptions that make up a 240-meter mosaic frieze inside the Dome of the Rock do not include Qur'an 17:1 and the story of the Night Journey, suggesting that as late as 692 the idea of Jerusalem as the lift-off for the Night Journey had not yet been established. (Indeed, the first extant inscriptions of Qur'an 17:1 in Jerusalem date from the eleventh century.)
Muhammad ibn al-Hanafiya (638-700), a close relative of the Prophet Muhammad, is quoted denigrating the notion that the prophet ever set foot on the Rock in Jerusalem; "these damned Syrians," by which he means the Umayyads, "pretend that God put His foot on the Rock in Jerusalem, though [only] one person ever put his foot on the rock, namely Abraham."
Then, in 715, to build up the prestige of their dominions, the Umayyads did a most clever thing: they built a second mosque in Jerusalem, again on the Temple Mount, and called this one the Furthest Mosque (al-masjid al-aqsa, Al-Aqsa Mosque). With this, the Umayyads retroactively gave the city a role in Muhammad's life. This association of Jerusalem with al-masjid al-aqsa fit into a wider Muslim tendency to identify place names found in the Qur'an: "wherever the Koran mentions a name of an event, stories were invented to give the impression that somehow, somewhere, someone, knew what they were about."
Ziad Abu-Amr explains the Islamic position:
...Jerusalem's multifaceted meaning stands behind the interest of Muslims all over the world in the land of Palestine as a whole. The city has strong evocative and emotional associations and has its own place in the hearts of Muslims. It is considered the third-holiest city in Islam after Mecca and Medina in Saudi Arabia. It derives its religious prominence from being the first Qibla, the initial direction toward which the Prophet Muhammad and the early Muslim community turned their faces in prayer. The direction was changed a year and a half later to Mecca by "divine command."
Jerusalem also derives significance from its association with Prophet Muhammad's miraculous nocturnal journey to the city and then his ascen¬sion to Heaven. This event is mentioned in the Koran in the first verse of chapter 17, "Glory be to Him, who carried His servant by night from the Holy Mosque to the Further Mosque (al-Masjid al-Aqsa), the precincts of which We have blessed, that we might show him some of our signs."2
In the nocturnal journey (al-lsra'wal Mi'raj) , according to Muslim tra¬dition, Muhammad was transported one night on a winged horse from Mecca to Jerusalem where he led Abraham, Moses, and Jesus in a prayer. Afterwards, Muhammad ascended to heaven accompanied by the archangel Gabriel. In this journey of ascension, Muhammad passed through the seven heavens where he encountered earlier prophets. The Dome of the Rock is the site from which Muhammad ascended. Although some critics argue that Muhammad's journey was spiritual and not physical, this journey has a three-fold significance:
First, it linked the city of Jerusalem with Islam in its very early days in addition to the sura which refers to Jerusalem as the first Qibla. Second, it inspired the Muslims with a bulk of lore, so much so, that Muslims all over the world celebrate that occasion every year. Third, it ushered in a new era in the life of the city because, from then on, the Muslims con¬sidered it their holy duty to protect it from the encroachment of the Byzantines and the Persians who were non-Semitic people.3
In addition, it is believed that a Koranic verse (v. 44 of chapter 43) was revealed in Jerusalem: "Ask those of our messengers We sent before thee — Have We appointed apart from the All-Merciful, gods to be served?”4
Can anything be added?
In an academic paper I just discovered, “Muhammad’s Night Journey (isra’) to al-Masjid al-Aqsa: Aspects of the Earliest Origins of the Islamic Sanctity of Jerusalem”, al-Qantara 29 (2008), 147-65, it is claimed that the Shi'a branch of Islam considered the Al-Aksa Mosque not to be in Mecca or Medina or Jerusalem but...in Heaven:
and he clarifies a theological point:
Read it all. And I suggest his book.
PS - Consider this, too.
By popular request, okay, ChallahHuAkbar suggeseted it, here's from Prof. Motti Kedar:
Jerusalem, too, underwent the process of Islamization: at first Muhammad attempted to convince the Jews near Medina to join his young community, and, by way of persuasion, established the direction of prayer (kiblah) to be to the north, towards Jerusalem, in keeping with Jewish practice; but after he failed in this attempt he turned against the Jews, killed many of them, and directed the kiblah southward, towards Mecca. Muhammad's abandonment of Jerusalem explains the fact that this city is not mentioned even once in the Koran...Jerusalem meant nothing to them.
Islam rediscovered Jerusalem 50 years after Mohammad's death. In 682 CE...Abd al-Malik, the Umayyad Calif, needed an alternative site for the pilgrimage and settled on Jerusalem which was then under his control. In order to justify this choice, a verse from the Koran was chosen (17,1 = sura 17, verse,) which states (translation by Majid Fakhri):
“Glory to Him who caused His servant to travel by night from the Sacred Mosque to the Farthest Mosque, whose precincts We have blessed, in order to show him some of Our Signs, He is indeed the All-Hearing, the All-Seeing. "
The meaning ascribed to this verse is that "the furthest mosque" (al-masgid al-aqsa) is in Jerusalem and that Mohammad was conveyed there...Thus Islam tries to gain legitimacy over other, older religions...Not surprisingly, this miraculous account contradicts a number of the tenets of Islam: How can a living man of flesh and blood ascend to heaven? How can a mythical creature carry a mortal to a real destination? Questions such as these have caused orthodox Muslim thinkers to conclude that the nocturnal journey was a dream of Mohammad's...
What are the difficulties with the belief that the al-Aqsa mosque described in Islamic tradition is located in Jerusalem? For one, the people of Mecca, who knew Muhammad well, did not believe this story. Only Abu Bakr, (later the first Calif,) believed him and thus was called al-Siddiq (“the believer"). The second difficulty is that Islamic tradition tells us that al-Aqsa mosque is near Mecca on the Arabian Peninsula. This was unequivocally stated in "Kitab al-Maghazi," a book by the Muslim historian and geographer al-Waqidi. According to al-Waqidi, there were two "masjeds" (places of prayer) in al-Gi'irranah, a village between Mecca and Ta'if - one was "the closer mosque" (al-masjid al-adna) and the other was "the further mosque" (al-masjid al-aqsa,) and Muhammad would pray there when he went out of town. This...is supported by a chain of authorities (isnad) [but] was not "convenient" for the Islamic propaganda of the 7th Century. In order to establish a basis for the awareness of the "holiness" of Jerusalem in Islam, the Califs of the Ummayad dynasty invented many “traditions" upholding the value of Jerusalem, which would justify pilgrimage to Jerusalem for the faithful Muslims. Thus was al-Masjid al-Aqsa "transported" to Jerusalem.