For Peter to get from Bet Zayit to the Old City of Jerusalem (assuming that there were any kind of tunnels that allowed him to do so) before the timer ran down (shown at just under 12 minutes when he started running), he would have to run the entire way at Usain Bolt's top speed (about 12m/s), the fastest speed ever recorded for a human runner.
There is no river close enough to Jerusalem for a dam to be built at Bet Zayit.
When Rabbi Lev and Joshua are watching the non-destruction of Al-Aksa, there are graves on the ground before them (the grave stones are visible. If Joshua were the High Priest, he would not be allowed near the graves.
Under Jewish law, all descendants of Aaron the High Priest are forbidden to enter graveyards.
When Emma and Margrove meet up in order to go get their treasures, there is a sea front visible on the other side of the car. There is no sea front in Jerusalem.
When Lynn is watching Al-Aksa not being destroyed, the building she is in is located on the Mount of Olives. This is clear due to the angle of the Old City visible from the windows.
The American consulate is in the neighborhood of Armon HaNatziv and since it is on the other side of the neighborhood from the Old City, has no clear view of the Old City from its windows.
Ambassador Rydell claims that the building is the American embassy. The American embassy is in Tel Aviv, despite laws passed in Congress requiring it to be moved to Jerusalem. Jerusalem only has a consulate.