In the beginning sequence involving the scuba diver in the tree, specifically when they are in the casino and the pilot says "All I need is a two." The dealer (scuba diver) lays down an eight of diamonds, but it is the only card in front of the pilot. In this style of blackjack, the player holds the first two cards in his hand.
At one point Quiz Kid Donnie says: "Samuel Johnson never had his life shit on... and taken from him, and his money stolen! Who took his life and his money? His parents? His mommy, and daddy? Make him live this life like this... A man of genius who gets shit on as a child!... " Actually all of those things happened to Samuel Johnson. He was a child prodigy who was exploited by his parents. His parents also stole of the money he made as a child prodigy.
In the "Wise Up" sequence, Claudia is dressed for her date, she's wearing black and her hair is up. When she opens the door to Jim, she's wearing red, her hair is down. On the way to the car, she is again wearing black etc, and at the restaurant she is back wearing red.
The view from the inside of the Barringer's apartment shows Sydney Barringer falling and being shot in the stomach as he passes by the window. However, the same incident viewed from the outside clearly shows Sydney falling with his feet oriented directly toward the apartment window as he passes it on the way down.
When Officer Kurring is leaving the station and walking to his cruiser in the beginning, he is carrying a shotgun. In the next shot as he steps into the cruiser, in the same hand he is holding a night stick and a flashlight, and no shotgun.
As Officer Jim drives in his patrol car, he has the windshield wipers on full blast because he can't see through the downpour. As the camera angle changes and we view the oncoming traffic, the oncoming vehicle's windshield wipers are not moving and the downpour seems no more than a mist.
When Officer Jim Kurring was driving near the beginning of the film, reflected in his sunglasses was a pair of hands holding the steering wheel. The reflection shows the steering wheel to be on the other side of the car -- not the side of the car where Officer Kurring was sitting. This indicates that the actor playing Officer Kurring was probably sitting on the passenger-side of the car while performing his lines and a crew member was driving the car for him. The film is then shown using the flipped mirror image.
When Linda Partridge is first placed in the ambulance, the EMT crew is not providing ventilations for her after stating that she has six respirations per minute (norm is 12-20). This would be priority and the crew should have been using an Ambu on scene. Such equipment is not seen until later.
During the weather transition about 2 hours and 22 minutes into the movie where "Rain Clearing, Breezy Overnight" is shown, The stoplights change from red, to yellow, to green. You can tell that the film was reversed in this scene, because stoplights change from green to yellow, and then red, not the other way around.
In the scene where Donnie Smith is robbing the furniture store he previously worked at the poster on the door reads, "Keep Door Lock at all times!", instead of "Keep Door Locked at all times!" Due to the owner's accent, it can be assumed that this was just due to him being a non-native English speaker and writer.
When Claudia brews a pot of coffee for herself and Officer Jim Kurring, she clearly holds the pot with two hands, one hand being on the glass and one hand on the handle. Since she is coked out and we can assume that she spends much of time under the influence, it can be assumed that she may not realize the pot is hot. Combine the effects of coke with the anxiety she is feeling for having a cop in her apartment and it is easy to believe.
She also clearly stated that the coffee had been sitting around and probably wasn't even hot.
The movie takes place when it is cold outside (we can see this from the clothes that the characters wear and from the visible exhaust from cars), yet the Partridge's pool is uncovered when the frogs fall. Assuming the pool is heated, this wastes energy, but is not impossible in a climate where the temperature does not approach freezing.