Continuity mistake: Frasier comes home to his apartment with a bottle of wine in a paper bag. He takes the bottle out and puts it on the table holding the bag in the other hand, but in the next shot we see the bag is already on the table and he is just placing the bottle down.
Continuity mistake: Marty, Frasier, Niles, and Daphne are in Frasier's apartment, talking about Marty moving in with Niles - M.'s beer can and remote are sitting on his little table. In one shot they are quite close together, but in the next the can has moved about six inches forward.
Continuity mistake: Eddie has been playing on Niles' couch, and the pillows are all over the place and there are a couple of other things on there as well. After Marty's chair arrives, Niles says to Frasier, "You have to take him back now," and suddenly the couch is all tidied up, with the pillows at the ends. A couple of shots go by and suddenly the couch is a mess again.