Tut's Case is Shut (2) - S2-E8
Continuity mistake: Tut's "pets," which are a little too obviously plastic, are crocodiles (with pointed snouts), and they're sitting on a grassy island in their water tank. The stock footage inserts, however, are of alligators (which have flat snouts) swimming in open water, with no island in sight. (00:02:30)
Tut's Case is Shut (2) - S2-E8
Revealing mistake: While Chief O'Hara is outside on the ledge of the top floor, King Tut commands him to use the flagpole to do acrobatics. When O'Hara obeys Tut, the vertical wire at the end of the flagpole is visible. (00:08:20)
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