Casey would not have been put in a police car after suffering such a severe leg wound, but after the initial dressing of the wound in the ambulance, she would have been transported directly to the hospital for treatment and a full examination because of the nature of the crime and the severity of her injury.
Casey is shown having been trained since she was a toddler to use firearms, yet when she does use a shotgun, she racks and fires on an empty chamber, even though she's shown looking at and then loading her last two shells.
When Dennis brings the girls' sandwiches, you see Marcia pick up half of the sandwich and take a bite, but as he leads the girls to the kitchen, the sandwiches on both plates are shown whole and there are no bites.
When Casey is loading the shotgun, it breaks over and loads from the breech. This makes it a single shot, but later on she is holding the gun and cocks it by pumping it. A breech loader only has capacity of one shell per barrel.
When Dr. Fletcher is giving her speech through Skype, you can see her being projected onto the large screen for the audience. The video on that screen is completely synchronized with the small image on the bottom right, but it should be delayed, as the video signal has to first travel there, be projected on the large screen, recorded by the second camera and finally sent back to her computer.
Note: If the internet speed is not an issue, it doesn't matter how many feeds its going through, it still travels at the speed of light and one would not notice any delay. Live TV shows have added a delay only due to the Janet Jackson incident at the Super Bowl.
In the close-up shot of Dr. Fletcher's degree scroll from Tulane University, the school of political sciences is misspelled as "political scineces". In addition, her degree of Master of Psychology would not be awarded by a school of political sciences.
When young Casey Cooke was in a make-shift hunting blind learning to hunt, it was obviously in the fall time because the ground was fully covered with colored leaves that had fallen from the trees. In the same scene, you can clearly see that all of the trees had thick green leaves on them indicating that it was not that late in the fall season.
When the Beast comes up from behind and grabs Dr. Fletcher, her glasses are present just above his arms. The subsequent shots when the Beast continually increases pressure, her glasses are no longer there.
The goof item below may give away important plot points.
The Beast is shown taking a bite out of Casey's calf, badly enough to cause her to limp for the rest of the movie; but, at the end, as her leg is being wrapped in the ambulance, the EMT grabs and squeezes her calf right where the injury would be. Casey doesn't flinch or react at all.
When Casey is running from the Beast, she is attacked in the gate between sections, causing her white shirt to be torn on her front and right (audience left) shoulder. When she is in the cage at the end of the corridor, she has to reload after firing and missing yet another shot. In the medium close-up on her left arm holding the shells, the sleeve is badly torn and dangles at her wrist. In the next shot, Casey gets frustrated with the same sleeve and pulls it off her shoulder to where it was at in the previous shot.