The cat's name is Sebastian Phillips Du Champs (Duchamp) and a urinal is on display as part of the art show. Artist Marcel Duchamp's most famous piece was "Fountain" which was a urinal turned on its side.
William Newman's last performance
During the montage of Randy listening to "Time After Time" repeatedly on cassette, the cassette player he's using has a transparent window revealing that the spindles which operate the tape are not spinning, therefor the cassette is not playing.