Revealing mistake: When Joe is strapped to the atom bomb he orders a girl to show him her boobies. When she takes her top off, you see a back shot of her (so you can't see her boobs) but her body is transparent and you can see Joe's arm through her body. Obviously, the girl was superimposed onto the shot.
Revealing mistake: When Joe is on the bridge and about to jump, the cop ropes him with a bungee cord. It's a single-stranded cord with a loop like a lasso. When Joe falls, however, it is a multi-stranded bungee cord with a proper ankle wrap. Obviously, it wouldn't be safe if the stunt man jumped with just a lasso, but it's obvious that it's two totally different ropes.