When Tree tries to fire the officer's pistol she is told by Tombs, "The safety is on". Tree had just removed the weapon from the officer's holster. Almost no police officer carries his sidearm with the safety on, they are always carried with the safety off.
When Tree tells Gregory that she knows about her wife and sets him free, it makes no sense for Gregory to threaten Tree with not letting her pass his class, as Tree could simply blackmail Gregory with telling her wife about their love affair.
When Tree escapes the hospital room she has slippers on, then after she sneaks by the nurses station & enters Gregory's office, she is no longer wearing slippers (barefoot), but in the next scene with Gregory & the killer, she's wearing slippers again.
In the second day during the lunch meeting, Carter once again spills chocolate milk on Tree. The position and amount of chocolate milk spilled across her shirt changes position and amount between shots.
When Tree is in her hospital room, there is a rack by the door containing three boxes of latex gloves, all size (S)mall. A real hospital room always stocks three different sizes of gloves: (S)mall, (M)edium and (L)arge, because one size of gloves does not fit all hands.
When Tree is attempting to elude the masked killer in the hospital parking garage, she flees in Gregory's silver Mercedes-Benz, using a floor mounted shifter, which that model does not have. In the US all Mercedes-Benz models come standard with a steering column mounted shifter.
When the police car is side swiped the black charger shows no damage to driver side at all. It should have have scrapes or broken mirror. And as the fire starts in crown victoria the gas is bubbling up around fuel door gas wont bubble up and there would be gas cap in way if it could. The gas would have to have come from behind body panel but damage was not enough for that.
It doesn't seem to matter how soon she decides to leave the dorm room after waking up. Even when she rushes out of the room the roommate shows up right away without any regard to the original conversation having taken place and her asking for some headache medicine. The environmental girl still walks up to her at the same time the sprinklers go off at the same time, The frat guy falls down at the same time etc. if she leaves the dorm so quickly she should be ahead of all of these events.
During the last day from the loop, how could Tree have the time to get close and so friendly with Carter, after what she just lived earlier in the morning ? Isn't she supposed to spend time with the police for interrogation or/and probably get arrested for murder charge against her room-mate Lori, until the situation and the investigation are clear and Tree exonerated?
Instead, she is free like if nothing was happened.
When she begins to investigate each day and follow one person to see if they're the killer, she keeps making a list and when the list is shown on subsequent days we see the other names already crossed out. This list needs to be made every new day Why would she keep making a list and cross off names again? She simply wouldn't put those names on any more lists. The scribbles marking off names are the same indicating that it's the same piece of paper. Not possible.
At one point, Tree plots out a way to kill Tombs. She goes to the hospital, pulls a knife on the officer, takes his gun, tells him that Tombs is about to escape and to go get help. She then goes into his room where he escapes, they fight and she shoots and kills him. She's then seen celebrating her birthday. There is no way that she'd be free that night - she would at the very least be charged with the murder of Tombs since there's no witnesses to see that he did in fact free himself. From an outsiders point of view, she took an officers gun, untied Tombs, and then killed him.
When Tree is at the hospital and Dr. Butler is giving her a physical checkup, he tells her that her injuries that were accumulated from her numerous deaths prior mean that she should already be dead. Tree deduces that this mean that the time loop won't be infinite and that she will eventually permanently die. This is a plot point that although is relevant in the alternate ending, where Dr. Butler's wife pretends to give Tree medicine for said injuries before killing her, it is never addressed again and forgotten in the theatrical cut, a result of bad editing.
The goof item below may give away important plot points.
When Tree shoots Tombs, she fires only three rounds before the slide is shown locked back. This indicates that the magazine is empty at that point. This pistol carries more than a dozen rounds in the magazine. No officer would ever carry only three rounds in their magazine, the magazine would be full.