Visible crew/equipment: At the diamond exchange, when Mr. Freeze and his goons are by the wall safe, the shadow of the boom mic is visible in the top right corner of the screen. (00:13:50)
Other mistake: When Mr. Freeze is moving through the room evaluating the diamonds, the tanks on his back can be fire extinguishers. There is no way that the "weapon" attached by hose to them will work, as the handles have to be squeezed to discharge.
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