The Sport of Penguins (1) - S3-E4
Deliberate mistake: After the episode intro, in the first shot we see the words "The New York Public Library" above the entrance to the library, where Barbara Gordon works. However, it's stated in S3xE1 that she works at Gotham City Library, and even in this episode when Penguin listens to the news about the bomb, it's noted as the Gotham Library. (00:02:00)
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