Visible crew/equipment: In the scene of Ram and Kurt's funeral, you can see Ram's supposedly lifeless body breathing.
Revealing mistake: When they show Heather Chandler in her casket in the funeral scene and everyone is praying, she's clearly breathing.
Continuity mistake: When Veronica and JD are in the kitchen making the hangover cure to kill Heather Chandler, they both screw the cap back on the Drain Opener. (00:25:10 - 00:26:05)
Continuity mistake: You can see the flash of light that signals them to react to the bomb going off.
Factual error: Slater had close to a dozen sticks of dynamite on him. At the very least they should have knocked Winona Ryder down, and made her deaf for a few days.
Continuity mistake: Heather Chandlers position changes in the coffin shot to shot when her friends are saying last goodbyes.
Continuity mistake: During the lunchtime poll scene, just after the three Heathers and Veronica leave the bathroom in the canteen, Veronica does not have the clipboard with the poll on it. You see her stare at J.D and she still does not have it, but when she begins walking towards him, it appears in her hands.
Continuity mistake: When Veronica is drinking her slushy while talking to J.D. about his bike, the cup is rotated differently in each shot. (00:17:00)
Continuity mistake: After Heather drops dead from drinking the poison, her body changes position between shots. In the first shot of her body (an overhead shot) she is lying on her left side with her right hand curled under her chin. In the next shot her body has rolled to the right and her right hand has moved away from her body. (00:27:55)
Continuity mistake: At the end of the movie, when JD is about to blow himself up in front of the school, JD and Veronica are talking in a normal tone of voice, and he seems to be standing only a few feet away from her, to her left. In the next shot, the camera pans a shot of the front of the school, and JD is right in front of Veronica, and 100 feet or more away from her.
Continuity mistake: When Veronica opens the locker of deceased Heather Chandler, there is a photograph taped inside of all three Heathers and Veronica. The photo shows the girls at Veronica's house, posed with their croquet mallets. They are wearing exactly the same clothes as they were during the croquet scene, and knowing these girls they would not wear the same outfits on the same day often. Which implies that it is supposed to be a photo taken from that day at Veronica's house. Now here's the mistake - how could a photo from that day be up in Heather's locker, when she died the next morning? The photo was taken on a Friday afternoon, and Heather never made it to school again.
Character mistake: At the football players funeral, the guy on the left is still breathing, despite being dead.
Other mistake: Right after Heather Duke and Heather McNamara drop in on Veronica and Betty Finn playing croquet, Veronica talks to her parents about the suicides. She still has a croquet mallet in her hand, so little time can have passed. Heather Duke rushes in with a shopping bag, and tells Veronica that while at the mall they heard about Martha Dumptruck's suicide attempt. But Heather Duke had just left Veronica's house - there wasn't enough time for these events to happen.
Continuity mistake: After Heather Chandler's funeral, Ram is fighting one of the geeks. In one shot, the geek's glasses are on. There's a cut away and when they show him again, his glasses are gone. (00:40:30)
Continuity mistake: Christian Slater is standing off to the right of the stairs when he is dying at the end. Suddenly he's in the middle of the bottom of the stairs when he blows up.
Continuity mistake: When Veronica confronts JD on the stairs going down to the basement, shots from behind show her pointing the gun at his chest, but pointing it at his head when filmed from the front.
Continuity mistake: In the scene after JD blows himself up, Veronica goes back inside the school where she runs into Heather Duke. Veronica then kisses Heather on her cheek, leaving a black mark on her face. In the next shot as Veronica walks away, Heather turns around and you can see that the black mark is darker, larger, and lower than it was in the previous shot. (01:38:55)
Factual error: After Veronica and JD give Heather the poisoned drink, she falls and shatters the glass table. The way that the glass breaks is not realistic. She doesn't fall far enough to cause the entire top to shatter into tiny pieces. Most likely, the top is strong enough that her body would rest on it.
Plot hole: Three gunshots were fired for Kurt and Ram's "double suicide" and almost two minutes pass between shots 2 and 3. Doubtful two police officers could think they shot each other.
Suggested correction: An officer could think that one boy shot the other twice, killing him with the second bullet, before that boy was successful in killing him. The remaining boy would then kill himself. "Shot each other" might be a sloppy description, but basically, Kurt and Ram are both dead. There is a letter - forged by Veronica - which "reveals" that they were a couple. No signs of anyone else being involved. The police consider it a "double suicide" because they believe the letter.
Interesting theory, but I respectfully disagree with your correction. Three gunshots to two dead bodies, each with one bullet wound, would arouse suspicion despite what a letter found at the scene says. If one of the boys killed himself, there would be some evidence to support that such as powder burns around the wound or powder residue on his hands. In fact, a forensic scientist would have performed a GSR test on the hands of the shooters to confirm they did in fact fire the weapons.