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.