Continuity mistake: Early in the episode Martin puts a piece of tape on the seat of his chair, before Frasier accidentally gets it thrown out. However later on when Frasier gets the chair back (and in later episodes) that piece of tape is missing. It's possible it was ripped off of course, but wouldn't Martin have replaced it again if there was a hole in the chair?
Continuity mistake: Roz has just received a call about Marty's missing chair and as Frasier comes into her booth, she is writing it down. As she says "I found the chair", she hands him the paper - but she goes from writing to handing it to him with no time in between.
Continuity mistake: In the episode "Call Me Irresponsible" from season 1, Frasier and Catherine are making out on Martin's old chair, which starts vibrating (probably because they inadvertently hit a switch on the side). But in "Give Him the Chair", Frasier tries to replace Martin's old chair by buying a new one which has a built-in massager. When Martin tries it, he looks horrified and says "That's disgusting", even though his beloved chair had the same feature.