Martin's birthday is coming up in this January episode. In the first-season June episode "My Coffee with Niles", Martin's birthday was also coming up.
When Niles and Frasier are sitting down in Cafe Nervosa discussing Niles' upcoming award ceremony, Niles pours creamer into his coffee but nothing comes out of the pourer.
Cappuccino is misspelled "cappucino" on the chalkboard that is visible behind Roz while she is talking with Niles in Cafe Nervosa.
Martin describes his late wife Hester as a person who was tolerant and loathe to criticize others. This hardly describes the Hester who threatened to kill Diane Chambers if she did not break her engagement with Frasier.
Martin pulls a beer from the fridge which is already open (foam on top of can), but makes the 'pull ring action' as if to open it.