Revealing mistake: In the scene where Frasier and Lilith meet in the living room, where Frederick has created a romantic atmosphere, Frasier has a long speech about how Lilith is not going to get him back, ending with "I need to be finessed!" and Bebe Neuwirth goes out of character and begins to giggle, before she quickly covers her mouth and pulls herself together. Though Lilith might have found Frasier's comment amusing, it would definitely not be in character for her to giggle like that.
Continuity mistake: Near the beginning of the show, Daphne comes home from shopping holding a bag of groceries with the leafy tops of vegetables facing out. Frederick goes to help her and suddenly the leafy tops are facing inwards, without Daphne having time to move the bag.