In one of the episodes, Crow pretends he's a skull to scare Mike. Once he does that, Mike goes and gets a golf club and starts beating Crow up. You can see Mike's left elbow knock off Tom's head. But Mike tries to compensate for it by "hitting" Tom.
The name of the episode is The Screaming Skull. I don't think that was really a mistake. Tom's head has popped off before, like in Mitchell (Joel's last episode) and in a couple of outtakes shown on the tape Poopie his head comes off several times.
I think that MST3K by nature can't have any slipups. In the theme song they even say "if you're wondering how mike eats and breathes and other science facts, repeat to yourself it's just a show, I should really just relax". I think the only valid slipup there could be is if you can see a puppet operators hand.
As I have said in other comments, in a show like MST3K, the sole purpose of viewing the show is to watch it and have fun. Lawndartz brought up a good point, that as they acknowledge in the theme song, paying attention to things like "Where does Mike get his food" and other circumstances like that are pointless.
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