Plot hole: Mola Ram has his men knock over a vat of water in a last ditch effort to kill our heroes. First of all the vat can't be that big if it can be knocked down with a few sledgehammers. Secondly, for the amount of water that chases Indy and co. down the vat would have to be big enough to fill the room it's in, which obviously it's not. Third, Indy and co. travel through several large caverns during the mine cart chase, caverns that could easily swallow up any of the water flowing through the tunnels so there shouldn't be any water left to catch up to Indy by the time they stop.
Plot hole: If the underground women really believed that Einstein and Copernicus were female, they wouldn't laugh at the quote of Marie Curie.
Plot hole: Superman (or Kal-El) was a baby when his parents sent him away from Krypton before its destruction, and as Jor-El told his son in his first message he would have already been dead by then for thousands of Superman's years. Kara never existed during any of this yet so somehow she instantly recognizes him from the poster on the wall, even though she should have no idea who he is.
Plot hole: When the doctors are discussing the condition of Bowman's mother, a newspaper headline on the wall displays the pictures of both Bowman and Frank Poole. These pictures are actually still shots of the two actors from an earlier conversation they had with HAL in the previous film. Since Discovery has been dormant for nine years, how did Earth manage to use these particular shots for the newspaper?
Plot hole: When Buckaroo is speaking with the president via video call (with John Parker by Buckaroo's side), New Jersey is explaining the reason humans can't see the aliens from planet 10, is a result of bacteria produced by the aliens which is then absorbed by humans via their olfactory senses, affecting their cerebral cortex. If this is the case, why doesn't the president see John Parker in his true alien persona. He can't smell him through the television. (01:04:50 - 01:05:40)