Continuity mistake: The butler and Frasier are discussing the new president of the opera board and Ferguson pours Marty a cup of coffee. In the next shot, over Marty's shoulder, we see he already has the cup in his hand, although there was no time for this to happen naturally.
Continuity mistake: Roz is at Frasier's soirée joking with Mr. Worth about selling him some giftwrap. Just before she says "everything but my bracelets", her drink and hat switch from her right hand to her left and her canapé from her left to her right. In the next shot they've switched back again.