Other mistake: When the setup for the first match is announced, the Ram is said to fight Tommy Rotten "for the strap", which is pro wrestling slang for a belt, meaning it was a title match. But after the match, which he won legitimately, The Ram is not announced as a new champion, nor is he ever referred to as such, and no belt is given to him after the match.
Continuity mistake: In the scene where Mickey Rourke's character has decided to wrestle again toward the end of the film, there is a sequence where you see him prepping to wrestle again, part of his prep is shaving his arm pits. When he arrives to the arena to wrestle, there is a brief shot of him sitting in a chair, in that scene he lifts his arms and you can see hair in his armpits.
Continuity mistake: When Randy is in the strip club talking to Cassidy about his daughter, and how she "ripped him a new a**hole", part of his hair is hanging down over his face. A few shots later (with Randy visible in each shot) his hair is back behind his ear, without him flicking it back or brushing it back.