Continuity mistake: At the party at Stu's house, when Dep. Dewey is walking through the house looking for the killer, Dewey walks into the living room with the TV and couch. Look at the TV, there is a white phone sitting right next to it. Later, when Sydney and Stu are fighting and she is about to push the TV on top of him, the white phone is gone. The TV also appears to be bigger. (01:40:40)
Revealing mistake: After Billy's stabbing, Stu charges Sidney projecting her through a doorway. In that shot you can easily see that Matthew Lillard is replaced by a stuntman. (01:40:15)
Revealing mistake: When Sidney discovers Tatum's body, we see her head intact, in particular the eye level. In her death scene, her cranium was being crushed right at the eyesocket. (01:07:25 - 01:22:15)
Continuity mistake: Mr. Himbry calls the two expelled students "Desensitized little sh*ts", pointing the open scissors at him. In the next shot he's looking at him but he changed position, since the scissors are gone from frame. (00:45:20)
Continuity mistake: Gale falls back on the unconscious Dewey after Billy kicks her. Her jacket is draped across the chest touching the white button of her vest. When Billy gets on his knees by her though, the jacket is fully open. (01:37:30)
Continuity mistake: Once Billy is done slashing his accomplice, he points the knife at him and tells him what to do; the knife hand keeps changing position between shots. (01:36:00)
Continuity mistake: Plummeting from the roof onto a boat, Sid causes a wetsuit (or a similar kind of fabric) to fall off. In the closer shot, the cloth is much more entangled than in the other view - look at the pink band. (01:21:55)
Continuity mistake: Off-balance on the roof as she shouts for help, Sid is hanging by the window with one hand or both depending on the shot. (01:21:45)
Character mistake: Sid deduces that Billy could be the killer because he could have used his phone call from jail to make the threatening call. However, the deduction has to be incorrect, since if it was really Billy, he could have never used the voice-changing device.
Suggested correction: This will sound pedantic (hey, it's MovieMistakes.com, we're entitled), but I don't think this is what is meant by a character mistake. Sidney isn't presenting an erroneous fact that goes uncorrected, she's explaining an idea that had crossed her mind. Billy immediately gives a plausible response and by the end of the film it's evident who'd called her. The takeaway isn't that Billy could still be the killer but that Sidney can't help but suspect him despite their reconciliation.
Other mistake: Tumbling down the ditch with Dewey, you can see that Gale loses her red pumps. In the rest of the scene though she goes to Mr. Prescott's car first and then back towards the street without fetching her shoes back. (01:17:55)
Continuity mistake: At the party, Randy asks (with a weird "yeeeeh!" that appears to be dubbed over) how many "hellraisers" are there. Matthew Lillard points at Rose McGowan two times in two different shots and not with the same hand either. (01:02:55)
Continuity mistake: Kenny passes the camera to Gale as she fetches the coat. The hand he used to slip her the camera joins the other hand on top of a plastic case, but in the next shot his right arm is again lowered. (01:02:45)
Continuity mistake: When Randy shouts overenthusiastically that there's a simple formula to the murders, the extras in the background change position in the next shot when there's a whole shot dedicated to their reaction. (00:56:45)
Continuity mistake: In the close-up when she tells Sid not to 'freak yourself out' because they have a long night ahead, the light on Tatum is wildly different from the rest of the scene. (00:54:30)
Continuity mistake: During the whole bathroom scene the trash bin by the exit door is oriented parallel to the wall or perpendicular. The mistake can already be spotted early in the scene when the cheerleader is berating Sidney, but it is much easier to notice it at the very end not just because there are multiple consecutive shots from different angles, but also because to make possible for Sid to collide with the bin as she slides across the floor, the bin has been placed almost two feet away from the wall. (00:46:30)
Continuity mistake: When some goof runs around the corridors of the school screaming, Neve Campbell's hair changes position over her shoulders between shots. (00:42:25)
Continuity mistake: Gale realised that Cotton is innocent, and she talks about it to the cameraman. In that part of the scene, the sun is on Kenny at a different angle in different camera angles (look at the reflection of the rays in his hair and jacket). (00:41:55)
Continuity mistake: When Sidney walks towards Gale's van to talk to her the day after she socked her, she passes by the same two students in two shots. (00:40:00)
Continuity mistake: Sidney's right hand is in a different position in the two shots that happen when Tatum's mother tells her that there's someone at the phone for her. (00:37:30)
Continuity mistake: Inside Tatum's bedroom, Dewey tosses Sidney an ice pack for her sore hand. Look at Rose McGowan's left hand; she's holding the plush bunny in a different spot between shots. (00:37:00)