At the time that this episode was written, only The Godfather (1972) and The Godfather Part II (1974) had been made. It predates the release of The Godfather Part III (1990) by three years.
Frasier wants a set of golf clubs as an anniversary present from Lilith, but he is never depicted as having any interest in golf during the entire run of Frasier (1993). He's only ever shown playing squash with his brother Niles.
The very first time that Woody comes to Cheers, he introduces himself and says that he's a friend of Coach. There's no mention of that when Coach's niece comes to the bar. Coach and Woody were pen pals- they never actually met in person.