Revealing mistake: When they shoot the killer at the end, the hole in his head is there before the gun goes off. You can see the hole in his head for about a frame before the flash of the gun goes off and his head drops. The body is also clearly a dummy. The scene then cuts and they show him being shot again. Once more, the wound is already there.
Audio problem: When they are having the conversation about Basic Instinct at the fountain after Sidney has been questioned, Randy's lips don't match when he says: "That was an ice pick, not exactly the same thing." (00:19:20)
Other mistake: After Billy Loomis and Stuart "Stu" Macher are revealed as the villains, they stab each other multiple times to appear as victims. Billy cuts Stu too deep, and Stu begins feeling weak and bleeding profusely from his wounds, showing that he may be dying. When Sidney (in the Ghostface costume) stabs Billy with the umbrella, Stu's rage takes over and he suddenly has the dangerous energy to battle Sidney in the living room. Stu nearly kills Sidney, until she pushes the TV on his head. If Stu was dying in the kitchen, how does he have all that energy to fight Sidney?