From my 13 yrs of living in Israel, most of it in Jerusalem, I seem to remember that the Cenacle on Mt. Zion, which Christian tradition says was the site of the last Supper and Pentecost was a medival church, now a mosque, though no longer used as such. Also the small mosque on the Mt. of Olives that commemorates the Ascension of Jesus now has a small mosque and I think is property of the waqf. The Cave of Eliyahu Hanabi at Mt. Carmel, is on the other hand, used, or at least was in the 70s by both Jews and Muslims. I think before the state of Israel there were many sites throughout the Hoily Land that were revered by both Jews and Muslims and sometimes Christians as well, ie. Al Khader, near Mar Elias.
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from the article: Share the Temple Mount