(at around 14 mins) Cliff sits and puts a napkin under his beer. When the camera flashes back, the napkin is gone.
(at around 11 mins) Diane orders "a couple of beers for the boys in the back room". Sam reaches for the glass rack hanging over the bar, but beer mugs are not kept up there, only wine glasses and martini glasses.
(at around 2 mins) A former Cheers customer named Leo comes in looking for Gus, a former owner of Cheers. Coach tells Leo he "will makes a few calls", and later informs him that Gus is dead. However, in #11.18 The Last Picture Show (1993), Gus returns to Cheers and works behind the bar for an evening. Though this would appear to be a continuity issue, it is easily explainable as Coach's source simply could have been wrong about Gus, or Coach himself could be wrong (as Coach often is wont to be).