Continuity mistake: When Lilith and Frasier are at Dr. Campbell's (the first time), he makes them tea. A shot shows him preparing it, pouring it, etc. But in the next shot, Frasier and Lilith are already holding their cups. There was not enough time for him to have passed them the cups.
Continuity mistake: Frederick appears in the kitchen to talk to his parents, who are ignoring him. In one shot he is covered with spots and in the next, he only has about half as many. He is supposed to have hives, which I know can appear and disappear quickly, but these look nothing like hives in the first place.