As Frasier singing the final words of the closing song for the Sea Bees, the camera angle shows that the teleprompter is prematurely blank.
Frasier's front door goes from being nearly soundproof where someone outside cannot hear someone talking right behind it, to instances like the one where Niles was distraught about his finances. Where he heard everything people were saying while he stood outside the door. There were several times where it from soundproof to almost like it's not there. In this episode he standing right next to it, and the woman outside the door doesn't hear anything he's said.
Roz's sister Denise recognises Frasier and greets him in the café. However, the only time they've met previously Frasier was pretending to be Roger, so she shouldn't know his real identity.
Roz's sister Denise recognizes Frasier as Dr. Frasier Crane, but in The Guilt Trippers (#9.23), Denise thinks that he is Roger, Roz's former boyfriend. It's possible that something happened between the two events but it is not mentioned in the series.