Continuity mistake: Trying to kill Sidney, Ghostface plunges into the front door of Delta Lambda a knife that is soaked in blood - even if they already cleaned ACICI's. Derek on the other side of the door looks at a knife that is mostly clean except a couple of tiny specks by the blade, and Ghostface pulls the knife back again bloodstained. (00:39:40)
Visible crew/equipment: Hearing about what happened at Omega Beta Zeta, Derek tells Sidney "let's get you home" and when she gets inside the camera comes closer to Jerry O'Connell for a dramatic shot...that catches in frame part of the stage light. Actually spotted by Wes Craven during the DVD commentary track. (00:38:35)
Continuity mistake: When ACICI apologizes for calling the guy "Ted" and says "I thought you were someone else" she is suddenly touching her left cheek between shots. (00:30:00)
Continuity mistake: Cici wrongly assumes his ex is at the phone and says his name; "Ted?" The blue pillow she's leaning her right part of the body agains changes position between shots. (00:29:35)
Continuity mistake: Gale massages her chin after she's hit, but does it alternatively with her thumb tucked under the chin or outwards, depending on the camera angle. (00:25:45)
Continuity mistake: Both when Gale speaks into the microphone saying "Tell us everything that's happened", and when she wags her finger at her motioning her not to punch her, her hand is at heights inconsistent between shots. (00:25:15)
Continuity mistake: Sidney and Dewey begin their chat. In the wide shot, you can see that a girl is passing by the gazebo, behind it. She does it again in the next closer angle on the two talking, starting from way back. (00:22:50)
Continuity mistake: When Gale tells Debbie off giving her a nasty 'quote', the sun shines on Laurie Metcalf's sleeve in the angle where she says "Great!" and does not in the ones before and after. She is left standing in dismay, and you can see her in background with the sun casting another entirely different shadow even if she didn't move. (00:20:05)
Continuity mistake: Debbie Salt introduces herself to Gale Weathers and asks her a question that Gale does not like, so much that she puts her hand on Joel's camera and points it away, downwards. At the cut though Joel's camera is back up. (00:20:00)
Continuity mistake: When Mickey mentions Godfather Part II, there are reaction shots on the other students who have to agree on that statement, but their positions are inconsistent between shots (for instance the girl with the blue shirt has both hands joined at first, then at distance, the girls on the background to her right are leaning towards each other at first, then not, etc). (00:17:00)
Continuity mistake: In her opening shot, CICI says that you can't blame violence on entertainment. Behind her, out of focus, there's a student with a beige shirt. You can see his left hand, but in the next shot he has his right arm crossed on top of it. The rest of the scene goes on with that extra's motions not matching at the cuts (he's touching his chin next time, then he isn't). (00:15:20)
Continuity mistake: When Sidney grabs the caller ID device, the position of her fingers on it change between shots. (00:12:30)
Continuity mistake: When Maureen's boyfriend reveals not to be Maureen's boyfriend at all, the height he holds his knife at changes between shots. (00:10:25)
Continuity mistake: When Maureen goes back to her seat and starts putting on her jacket, the dude at her side begins waving his arm super-enthusiastically making happy coos. She finishes putting her jacket on and the guy, who is still making those sounds in dub, is sitting composed. (00:07:05)
Continuity mistake: When Maureen and Phil arrive in the theater, immediately at the beginning before the camera even gets fully in focus you can see by the door a blonde girl putting on the Ghostface hood, with her partner helping her. The camera cuts away for a second, and in the next wide shot you see her repeating the gesture. (00:01:40)
Deliberate mistake: It's a humorous twist that Randy's killing is covered up by some random guys passing by with a ghetto blaster, but there was dead silence when Randy was talking earlier; not being in frame does not block soundwaves. (01:05:15)
Character mistake: Dewey says that it does not make sense that the killer, who at this point is characterized as a copycat of the Woodsboro team, attacked Sidney. Actually that's exactly what happened in the first Scream; after Casey and her boyfriend, Ghostface tried to kill Sidney. Dewey should know since he was the first responder on that call doing a puppet show at the door, and it's not only amazing that he wouldn't remember, but also that nobody corrects him and that they haven't run a timetable of the previous events at all. Of course in the end the pattern does not matter just as Dewey later says, but up to that point, the killer was following it to a T, so they are reaching the conclusion too early and against the evidence. (01:01:00)
Other mistake: Ghostface tries to kill Sidney by the front door of the sorority house, and the pendulum clock shows it's 12:10, which fits also the timeline with CiCi's murder. Running away from him though, Sid passes by a mantle in the party room that has a clock that strikes 10 to 7. (00:39:40)
Character mistake: Mrs. Loomis is crazy and does not really think things through (she finishes her speech saying "who gives a f..." and that she's untraceable anyway), however it's worth noting that when she tells Sidney the official version that the police will believe, she is wrong; she says it wiping the gun clean from prints and throwing it away, which means that the police would find the supposed murder weapon with neither Mickey nor Sidney's prints on it, and neither wears gloves. Moreover, she plans to disappear and she was prominently featured in the media coverage, so people would certainly investigate her at least as victim.
Suggested correction: I don't think that a psychopathic character acting irrationally and jumping to unlikely conclusions really constitutes a character mistake. But I do think it's also worth pointing out though that cops usually don't rely on fingerprints on guns anyway - the likelihood of finding a usable print on a gun is minuscule (only about 5%), and there's going to be traces of things like skin-oil and whatnot on it from being handled, so the cops will likely just assume it was used by someone in the room - the most likely candidate being either Sidney and Mickey. Mrs. Loomis is also using a false identity and has got surgery to change her face before, so she could likely disappear pretty easily. Real-life killers get away with disappearing all the time.
I am no expert in true crimes and forensics, I am just challenging the movie logic here (which is why I talk about the behaviour of a crazy character who is running exposition). What I get from your objection though is that the cops wouldn't be able to tell that she wiped the gun clean from prints and so that wouldn't stick out as suspicious? She didn't really change her face, since Sidney recognizes her when she gets a good look at her. Rewatching the scene anyway it's very evident that she does not really care because she simply puts her faith in the cops not being able to track the fictitious Debbie Salt, so I would be happy with a correction here, I was interested in pointing out that the whole first part about wiping the prints and throwing the gun aside does not seem to logically follow up, I take note that according to your objection using 'real science' and forensics practice it might not even be that.
Character mistake: The library of Windsor College is awful at cataloguing, since Sidney searches the "Social Sciences" section and her screen is full of books about Quantum Physics. (01:06:35)