Continuity mistake: When Roz and Frasier are in Bebe's office, and Frasier is exclaiming about her taking digitalis, the water glass in front of her is empty. The rest of the shots show it being about half full, even though she never refilled it, and there was no water source to be seen.
Continuity mistake: At the beginning of the show, when Niles and Frasier are in Cafe Nervosa, the man behind them has a paperback book which is open with all the pages fanned out, and then it is lying flat, then fanned out again, and so on. It is not a case of him changing the book naturally, as the positions of other things in the shots change slightly as well.
Continuity mistake: Frasier meets Heather in the bar. She is reading a book which she has propped open on the bar, but as they talk, she takes it off the bar and closes it in her lap. A couple of shots later we see book is back on the bar and she is closing it again.