Continuity mistake: In the scene where Martin is trying to find some aspirin and appears on the living room mezzanine, John Mahoney is wearing glasses (Martin wasn't wearing glasses at this point). In the next close-up shot the glasses have disappeared. (00:04:40)
Continuity mistake: Frasier and Niles are at the Shangri-La, looking at an apartment for Niles. While they are standing in front of the closet, sometimes the door is open (revealing the former tenant's clothes inside) and sometimes it is shut.
Continuity mistake: Near the end of the show, Niles has signed his lease for the Shangra-La with his Noel Coward pen and he puts on the table next to the lease. A couple of shots later we can see the pen lying on top of the lease, even though no one touched it.