(at around 1h 30 mins) When Sidney is in the police station, she's on the phone with the killer on a cell phone. When the killer hangs up, you can hear a dial tone. You wouldn't be able to hear a dial tone on a cell phone.
(at around 23 mins) When Sarah Darling is in the empty production offices of Sunrise Studios, she is looking for Roman Bridger, the director of Stab 3. However, when Sarah calls for Roman in an office, she clearly says, "Ronan," not "Roman."
(at around 1h 28 mins) When the killer calls Sidney while she is at the police station, the word, "Nokia" is visible on the bottom of the phone. In the next scene it disappears, and then reappears in a later scene.
(at around 1h 5 mins) On the hot set of Sidney's room the longest side of the table is flat against the wall with the bed. When Ghostface is thrown from the false door above the set, the table is rotated with its shortest edge against the wall with the bed, making the bed closer, so Ghostface could land on it.
Sidney is wearing black, high-heeled boots in the middle section of the film, but does not appear to be wearing them while waiting in the police station later in the film when the killer calls her. However, in the last part of the film, when Sidney arrives at the house, she is wearing boots again as she can be seen pulling not one but two guns from them.
(at around 1h 7 mins) When Sidney jumps out of the window in the Sunrise Studios, and Dewey comes to her, there's a point where she is looking down, and the camera angle changes to show her looking right at Dewey.
(at around 1h 5 mins) When Sidney goes through the door that leads to nowhere, she holds on and grips the wall frame. She could not have closed the door from her location because it was almost fully open and out of reach (though some viewers have claimed she could have used her foot).
(at around 1h 25 mins) After Jennifer's death, Gale is attacked and uses her leg to push herself and the killer down the basement stairs. They fall in, and it is shown that the door opens inwards, but in the next shot, the door is shown to be closing inwards from the outside.
(at around 9 mins) In Sidney's first scene, she enters 1288* on the alarm-system keypad on the road gate, and then twenty seconds later enters 1288# on the alarm-system keypad inside her house on the wall next to the door. It is entirely possible that 1288* arms the road-gate alarm and 1288# arms the house alarm.
(at around 44 mins) In the "....whoever smells the gas" scene the killer has cut the power to the house, but the pool lights remain on and the fax machine works. An uninterruptible power supply (U.P.S.) is plainly visible next to the fax machine, which may be unusual, but certainly makes it possible for faxes to be received and printed.
(at around 1h 5 mins) When the killer chases Sidney through the set, Sidney opens a door that leads nowhere and climbs through it to the side of the set out of view of the camera. The killer would have known the door goes nowhere, but it would not have stopped the killer from opening it. The killer falls because Sidney pulled the killer's shirt.
(at around 6 mins) When Christine is running from the killer, she locks herself in a room. The killer makes a single thin linear hole in the door with his knife, but he then twists the knife, turning it into the circle we see later.
When Sidney, Dewey and Gale meet Martha, Gale does not know who she is. However, earlier in the film, Dewey and Gale discuss how Gale lived with him in Woodsboro until after he recovered from the injuries he sustained at Windsor College. Therefore, Gale would no doubt have met Martha, a close friend of Dewey's, already. Martha even tells them: "We miss you in Woodsboro, guys."
The goof items below may give away important plot points.
At the beginning Cotton is talking to his publicist Andrea. He is saying he won't do a cameo for Stab 3 for less than $1 million. But when he is killed and Sidney overhears the news report, the reporter says that he already finished filming his cameo.
(at around 31 mins) Jennifer says she is next to die in the script of Stab 3, which Dewey confirms. However, when Jennifer is about to be murdered (at around 1h 24 mins), she says "You can't kill me. I'm the killer in Stab 3." Jennifer is saying what she hopes will stop the killer from stabbing her. In addition, there were three versions of the script, and she might have been the killer in one of them. Also, she may have been the killer in the script and seemingly dead, but not actually dead, like Billy Loomis in Scream.
(at around 1h 45 mins) In the final fight between Sidney and the killer, she stabs him in the back with an ice pick. Then she picks up his knife, but only to throw it out of reach. She can be seen removing the ice pick before stabbing him with it a second time.
In the opening sequence when Cotton is murdered, the room he and Christine are in clearly has a skylight in the ceiling, but once Cotton is thrown over the desk and looks up at the killer, there is no skylight. It is because two different opening scenes where shot, and the end of the scene when Cotton is looking up at the killer took place in an entirely different room.