The Entrancing Dr. Cassandra - S3-E25
Visible crew/equipment: After Batman discovers Cassandra's true identity in the alchemy book, he takes a call from Commissioner Gordon on his cute portable Batphone, then he and Robin head to Spiffany's. When it cuts to Spiffany's, just as narrator William Dozier says, "Gotham City's fashionable 15th Ave," the actor's white marks are visible on the floor under the table. Then we see Cassandra's and Cabala's white T-marks when they walk in. Next, upon the Terrific Trio's entrances, we see their T-marks as well. (00:08:25)
The Entrancing Dr. Cassandra - S3-E25
Visible crew/equipment: While Batman and Robin are at GCPD, Batman decides to use the library to research occult sciences, and when it cuts to Cassandra and Cabala returning to their hideout they walk over to the table, and behind them we can see the chalk marks on the floor by the door, where they previously stood. (00:05:15)
The Entrancing Dr. Cassandra - S3-E25
Visible crew/equipment: After Alfred has placed the two-dimensional Terrific Trio into the Three-Dimensional Bat-Restorer, when they all walk out of the chamber, two chalk T-marks are visible on the floor. First we see Batgirl's T-mark and then Robin's. (00:16:50)
The Entrancing Dr. Cassandra - S3-E25
Continuity mistake: The Batmobile returns to the Batcave by remote control. It's facing left when we get a brief, three-second shot of Batgirl talking to Batman and Robin. In the very next shot, the Batmobile has instantly turned itself around and is facing right. Its turntable (which was actually pushed manually by stagehands under the platform) didn't work quite that fast. (00:18:05)
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