Continuity mistake: When Shane first gets into Studio 54, he is told to take his shirt off. He pulls it over the top of his head. Then he walks in holding it and even though he never unbuttons it, it is somehow unbuttoned when he puts it on again.
Factual error: When the command module, with the engine shut down, is in earth or lunar orbit or in trans lunar coast (external shot), you hear a rumbling sound. It's in a non powered coast, so there shouldn't be any engine noise.