When the girl is trying to escape from the gas station attendant at the gas station, she drives off with the pump still in the gas tank. The next shot of her vehicle shows a rear shot of the SUV and the gas cap is screwed back into the gas tank.
In the opening scene at the gas station, Michelle is wearing heeled black boots, but when she leaves the gas station, feet with different shoes are shown in the close-up of the pedals (which are the pedals of a much older vehicle). The shot is taken from later in the film.
At the Frat party, Paul and Natalie are sitting talking about what's going on. Paul puts his hand on Natalie's face and Natalie then puts her hand on Paul's wrist near his thumb. As the shot changes from Paul to Natalie, her hand appears and disappears with each shot.
When the campus police lady slips on the large puddle of blood in the professor's office, her whole back side should be covered in blood but in later scenes there is no blood on the back of her pants or coat.
Pouring rain falls when Paul, Natalie and Brenda leave campus and then stop at gas station. But few minutes later when Natalie and Brenda run from gas station in the forest grass, shrubs and trees are absolutely dry.
In the opening sequence, near the end the woman is driving away and the vehicle is moving at high speed along the road, yet when the axe crashes through the window, the vehicle is sitting still. This is impossible; a stop that abrupt would have sent anyone not wearing a seat belt through the windshield and regardless, it would have taken some time for the car to come to a complete stop anyway.
Blood congeals after half an hour exposed to oxygen; it is therefore impossible that the character's wrists would still be bleeding enough to soak through the white sheet that the coroner's men put on her in the morning.
There is not only no way that Natalie's roommate could have written such a lengthy note without collapsing from blood loss, but also no way that anyone would have assumed that 'no foul play' had taken place; additionally, a security guard from the school would not be sufficient to make that sort of pronouncement in any case, and actual police investigators would be involved in the case of any such violent death. Natalie even mentions the message, which would seem to showcase a tremendous oversight in writing.
While it was probably added for tension and to introduce a greater conflict, the dean's actions to both Paul and Natalie would likely have cost him his job. Her 'criminal record' -- clearly stated to have been an action in high school -- would have been cleared upon her 18th birthday and majority, as per juvenile offender regulations. The dean would have had some difficulty even discovering such information unless he had been looking specifically for it (and likely violating a number of laws), but in any case it not only would have put his position at risk, it also was utterly irrelevant to the allegations Natalie had brought against Wexler and may have been a violation of Natalie's rights. Another instance in the film where involvement of the authorities was conspicuously ignored and characters seemed to happily overlook the very obvious problem with the situation.
In the final scene, the lead character's abdomen is seen being cut open with a scalpel. We then see her scream in pain. Minutes later, she is no worse for wear, considering the major incision in her stomach. There is no more mention of this "pain" for the rest of the film because the scene was added at the last minute.