Other mistake: Much like in the original Scream, an absurd amount of time goes on since the time when Dewey is left for dead (they broke into the school at half past nine according to the clock) and when first aid is administered (the morning after).
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.
Other mistake: The movie is supposed to happen "a couple years" after the previous (words of the moviegoer behind Jada Pinkett) but the current date shown at the theater says 1997, and Scream was set in September 1996 (calendar at Stu's house distinctly visible when he brings Sid's dad out of the closet).
