Despite having teamed up effectively with Niles when he filled in for a sick Frasier in the previous episode, Frasier says that Roz "despises" him because he "barely acknowledges her existence."
Daphne uses the expression 'bumbershoot' to describe her umbrella, claiming it's a British term. In actuality, the word only is purely an American invention, and only appears in American English dictionaries. (A real example of a British colloquial term for "umbrella" would have been "brolly".)
Roz calls herself "ecumenical" after saying she doesn't "care if they're Jewish, or Jehovah's Witness or Buddhist." The word "ecumenical" relates solely to Christianity.
Niles pronounces 'Bruno Magli' with a hard 'g'. In future episodes, Niles is established as an operaphile who has logged extended vacation time in Italy; it hardly seems likely he would make such a glaring mistake in Italian pronunciation.