Factual error: The Bat signal at the end would not show up like it did in the film. In order to be as clear as it was, as well as visible, it would actually have to shine onto a surface, not just the clouds. They made this same mistake in Returns, but made it believable in the clouds (just not as sharp) in Forever.
Factual error: It would take even a very strong acid a lot longer than a few seconds to eat through the thick metal bolts holding up the bell. (01:44:00)
Answer: He could have looked up her address in the phone book. Just before Bruce arrives at Vikki's apartment, Joker asks Bob the Goon for - a phone book. Also he could have been tailing Bruce and found her apartment that way, after all he does show up not long after Bruce does.
Alan Keddie