Cheers and Wings have a very long chain of cross-overs. Therefore, their universes are the same. However, Hugh Maguire plays Hugh on Cheers, and an unnamed businessman on Wings.
Goof: Brian asks Alex out on a date and for someone who wasn't at all interested in later episodes she quickly agrees. What's even more strange is the fact that no further mention is made in this episode of how the date went or if it happened at all. Nor is the date ever mentioned again. In fact in future episodes featuring Alex, it's back to the usual routine of the guys chasing her and her playing particularly hard to get.
Goof: Lowell picks up a hot frying pan without an oven mitt.
After discovering Helen has eaten the oreos, the gang forces open her mouth to show her darkened teeth. In the very next shot her teeth are perfectly clean.