Revealing mistake: Right at the end of the obligatory Bat-rope climb scene, look at Robin's cape; the wire that is used to keep it in place (aka sticking out to make it look like it is subjected to gravity and drapes down) loses position too soon, so the real gravity causes the cloth to go towards the wall the dynamic duo is supposedly walking vertically on. (00:11:30)
Revealing mistake: The newsreel shows several issues of the imaginary Gotham City Times. Nice job with the headlines and the page layout, but every single one of them is issue number 11. (00:14:00)
Answer: There wasn't one singular city used. It was shot in and around various locations in California, plus on a lot of sets and backlots. Ex. Some scenes were shot in LA, some in Pasadena, some in Santa Barbara, etc.
TedStixon