Revealing mistake: When they show Heather Chandler in her casket in the funeral scene and everyone is praying, she's clearly breathing.
Visible crew/equipment: In the scene of Ram and Kurt's funeral, you can see Ram's supposedly lifeless body breathing.
Character mistake: At the football players funeral, the guy on the left is still breathing, despite being dead.
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.
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.