Plot hole: When we first see the reanimated Sparky, his head's sewed on. While that makes him look a bit like the traditional Frankenstein monster, it doesn't make a lot of sense - the original monster had stitches on its neck because it was made from multiple body parts, but it's not like they sawed the dog's head off after it died...
Suggested correction: Do we ever see how much damage the car did?
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: When Arnie is driving the cop car and shooting at Conner and Reese, 5 or 6 inch holes from the gunfire are shown in the door right beside Connor. If the shell penetrated the steel door (which it could easily do - and was shown to do), there's nothing inside the door or on the other side of it to stop the bullet. Connor, and probably Reese, would've been ripped to shreds.
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: 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: Captain Bosch and AJ steal George Cooper's photos, but not the negatives. George Cooper discovers the photos are missing, and could have just recreated the pictures from the negatives. He is looking for who took his pictures later. (00:37:30 - 00:53:00)
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)