The only place where you need to go through a scanner in the old city (of which only a half is actually in israel), is at the wailing wall, and only if you go in through the entrance at the muslim or jewish quarters (the main entrance does not have a scanner). This is a "hand bag" strength scanner, and you should be fine passing most film through it, though in most cases with some patience, you can have it hand inspected, just don't be in a rush.
Some bags used to be randomly scanned with a similar scanner at the Jerusalem central bus station, but that might have been stopped by now.
The coptic church is dark, and harder to shoot at because it is also smaller.
see some work on film shot there (and other places) http://www.galitibbon.com/
The dome of the rock mosque is brilliantly lit, and is one of the most exciting places to shoot, it is closed to Israelis (and jews, but you do not have let anyone know if you are), and if you have a chance you should most definitely go. Its all withing walking distance, so is the wailing wall.
Buying film in the old city is possible, but it will be mighty expensive if you can find any.
Eat hummus at Lina restaurant!