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)
Continuity mistake: When Sidney punches Gale in the face, she flies back against her cameraman that catches her putting his hand on her side under the armpit. In the next shot Kenny's hand is on the upper arm, and Gale is also already holding her cheek. (00:36:35)
Continuity mistake: When Gale Weathers 'interviews' Sidney in the back alley, the microphone is turned at different angles between shots. (00:36:30)
Continuity mistake: Tatum is growing impatient while Sidney is sitting in the police station waiting to be released, and she hurries her brother. In this sequence there is a blatant lack of continuity whenever the editing switches to reverse shots, as Rose McGowan's hand and Neve Campbell's movements don't match between angles. (00:35:25)
Visible crew/equipment: When the officers take Billy away from Sidney's house, a set of lights is reflected in the back window of the car. (00:31:00)
Continuity mistake: Sidney is rather inexplicably covered in blood when she reappears to stop Gale from driving off in the news van without her (even her hair is drenched!). It's true she'd been off-screen for a while and who knows what's happened to her, but it's hard to come up with an explanation from what we've seen, especially since the implication is that she's simply been hiding out in the fields this whole time.
Other mistake: During Tatum's murder we see some problems exacerbate. The killers are not supposed to be invulnerable and are wearing a cheap costume, but they receive hard hits (Tatum breaks two bottles of beer, one straight to the face) and they don't have a single scratch. When she is killed, nobody hears her scream and nobody else needed to grab a beer either. Furthermore, Ghostface has the garage door fully open, but without knowing who is on the other side, that is one room away from the others, goes by the mysteriously unlocked door to the inside of the house. And we see Billy (who should be the killer there, since Stu was at the party) join in coming from outside.
Revealing mistake: Sidney is teasing Billy, and as a sort-of-reward to him she flashes him before he goes. That's the idea, but in the view from behind you can actually see through the nightie the shoulderstrap of a bra. (00:16:55)
Suggested correction: Could she have had a bra that undoes at the front and quickly flashed him?
To actually answer the question; her hand is on full display, holding the nightie open. She'd still have to open the bra. You can technically argue that you can't see her other hand, which she could be simultaneously maneuver to pull down the cup of the bra and expose a nipple, since there's hardly any time to undo it fully and she'd have to fasten it back afterwards. Or that cupless bras exist. Truth is, she opens her casual, normal, comfy nightwear during the unexpected visit of her boyfriend, and the way the scene is shot leaves no room to interpretation.
This is a question, not a correction.
Factual error: Throughout the movie there is constant reference to the Sheriff; Burke is the sheriff, Dewey works for the sheriff (and he will become the sheriff in Scream 4, with the same mistake happening), but the car Dewey uses is marked "Woodsboro Police."