Continuity mistake: Near the end of the show, Niles and Frasier are shaping hamburger patties in the kitchen. Niles has a blue bottle of water which sits on the stove top in front of him. In one shot it suddenly appears on the counter to his right; even though Niles hadn't moved it. By the end of the scene it is back in front of him on the stove top.
Continuity mistake: When Frasier and Niles are in the restaurant, Niles is under the influence of medication. He lays his head down on his arm just as one of the geniuses arrives and greets them. In the next shot, his head is lying right on the table, with no time for him to have switched positions.