Revealing mistake: When Nancy is running up the stairs in her house to escape Freddy for the first time her foot hits the steps and go through the steps into some goop. Look at the steps above that step and you can see the pre-cut holes where the next sets of goop will be. (00:39:10)
Revealing mistake: When the Russian pod is launched, a wide shot shows the Monolith at top/right with Jupiter in the background and both the Leonov and Discovery at bottom/right with the pod nearby. Just before this shot ends, all three spacecraft vanish, leaving only Jupiter and the Monolith for a very short but obvious moment. (01:04:35)
Revealing mistake: Near the end, Clint Eastwood picks up a lamp in anger and throws it across the room, but there's no power cord attached to the lamp.