Revealing mistakes: As the train is arriving in San Francisco at the start of the movie, the rear-screen exterior is backward. Notice the lettering on the buildings.
Continuity: When Dancer sees that Nora is going to use the pay phone (in the Lichee Club), he approaches the hat check girl to load her up with coins so that she can keep Nora from using the pay phone. When Dancer first approaches, the hat check girl is sitting in a chair, facing toward Dancer. Dancer continues to approach and she is now standing by the counter, facing away from him.
Revealing mistakes: As Nick shines his pen-light on the names outside the apartment building, the light falling on the wall is out of sync with his movements.