When Frasier misses his cue to go to the news break at the end of his show the music for it bleeds into his broadcast. This may be the only time in the series when any other sounds: theme music, segues, PSAs, news, advertising, etc. can be heard outside his booth during his broadcasts.
The final scene mirrors the ending of Casablanca. Only one of the two lovers can ride the cart/plane. The cat's name is Louie, like the French police officer in the film. Frasier quotes Bogart's "beginning of a beautiful friendship" line, which concludes the film.
Frasier says goodbye to Kate at Gate A7. This is the same gate at which he meets Laura (a woman he meets only by virtue of her mistakenly leaving messages on his answering machine) in season four's Odd Man Out.
Niles says normally he bleeds like the Russian royal family. They were famously hemophiliacs-a disease that doesn't allow blood to clot, so you wouldn't stop bleeding.