Continuity mistake: Frasier is on the phone at KACL with Jerome's girlfriend and the reflection in the glass shows him raising his hand to his face, but the next shot returns to him - his hand is on the console. There was no time for him to have shifted positions normally.
Character mistake: In the scene where Jerome Belasco turns up unannounced at Frasier's apartment, Daphne tells him she's psychic and guesses that he's an osteopath. After Jerome leaves, Daphne says she thought he seemed very nice. Frasier turns to her and says, "This from the psychic who said he was a chiropractor."