Numerous times during Cliff's retirement party, his beer switches between having a rather large head of foam, and having no foam at all.
Martin tells Cliff that he had been a police officer for 30 years. Earlier in the series, it was established that Martin had over 40 years service.
Phil, the well wisher whom Cliff accidentally calls Al, says that Al has been dead for 14 years. Al Rosen, the actor who played Al, made his final Cheers appearance in 1989, meaning that he cannot have been dead for more than 12 years.
As Carla is talking to Niles, she relates the story of the Cheers gang taking Frasier snipe hunting as a gag. In spite of her saying that snipe do not exist, there actually is a wading bird called the Snipe.