The snatch of dialogue Frasier recites from Agatha Christie's play, TEN LITTLE INDIANS, is fictitious; no such dialogue exists in the play.
When Martin sits on the new vibrating chair Frasier bought, he comments at it being disgusting but earlier in the season his own chair had to be plugged in for it had a built-in vibration feature. Response: It was two different kinds of vibrating chairs. Martin's chair has a shaking vibration. The new chair had a quiet vibration that likely pushed something into the body.
A KACL caller informs Frasier that his father's chair is on a high school stage. When Frasier goes there, the only adult present has never heard of the Frasier Crane Show. So who placed the call? Response: A parent who dropped off a student or a janitor or anybody. The caller did not need to stay until Frasier arrived.