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)
Continuity mistake: When doctors are discussing the medical condition of Dave Bowman's mother, a close-up of the African-American doctor shows a framed newspaper on the wall behind him. It is the front page and has prominent pictures of Bowman and Poole taken during their mission. In the next, wider shot, we see this wall suddenly has nothing on it - the newspaper and frame have vanished. They return when Bowman's mother sits up in bed. (01:16:45)