I think it's the scene where Rimmer is looking down his trousers that implies he's actually in the mirror!Rimmer's body. If he was still *him* he would still have the same tackle, right? And if it's the process of crossing over that changes him, why didn't his personality change as well?

Well, technically, Rimmer could have backed out and exposed his deception. If he was more worried about his life then anything else of course.