When Claire gets home after the blind date, she sits on the couch and takes out her ponytail. In the next scene, her hair is back in a ponytail.
When Vicky runs up to interrupt the fight between Noah and Jason at school, she's wearing a dress. In the next scene (which takes place immediately afterward) she is in her office reprimanding Noah and is wearing a completely different outfit.
When Kevin is driving with Garrett, the seat belts appear and disappear throughout the drive. Shots from outside the car show seat belts while shots inside the car do not.
Noah had severely injured his fist, punching a wall in anger, however when he appeared in Claire's house later that day he had no dressing, nor any marks on his hands.
The scene when Kevin suffers a severe allergic reaction and Noah retrieves Kevin's Epinephrine injector, shows Noah holding the unit with the safety cap still in position. In addition, the needle extracts while the safety cap is on (which should not be possible) and the needle should not be able to protrude as far out as the scene shows.
Erasing a video file on a computer does not automatically permanently delete it. Even without a backup, files can be retrieved.
Noah brings Claire a copy of The Iliad, which she notes is a "First Edition." Being a story passed down through oral tradition, and not committed to print until it was 1,000 years old, it would not have had a First Edition. Being in the public domain, it could be (and is) published by numerous companies. Being classical literature, however, as opposed to modern, it is doubtful the company would have made much note of it being their own first edition of the text.
There is no way that Claire can afford to own a Cadillac on a teacher's salary.
When Noah and Kevin are shooting oranges, the delay between the shots from the gun as Noah fires and the oranges actually jumping or exploding from the hits are far too long. This shows the gunshots were set up using blanks in the gun and squibs in the oranges.
Allie's family's hardware store is called "Calahan". In the credits, Allie's surname is spelled "Callahan".
In the scene where the Challenger crashes, the car is heard to accelerate even though the driver's foot was not on the accelerator.
When the EMTs are loading Kevin into the ambulance after the climactic barn fight scene, you can very clearly see the camera in the reflection of the window of the ambulance for two or three seconds.
After Noah defends Kevin from his bullies by beating one of them far too much, Vicky keeps Noah in her office and says that the bully's skull has been fractured. Despite such a serious violent assault during school time and on public school property, Noah does not seem to face any consequences from either the school or the local police. He is not arrested or held accountable to the injured teen's parents or even questioned by any one other than Vicky, the vice principal of the school.
The minivan is shown hitting a semi trailer carrying a pipe and instantly exploding. That is impossible. Even if there had been a fuel leak it would take some time for the fuel vapor to find an ignition source. Also, the explosion came from within the passenger compartment of the minivan, which would likewise be impossible unless it was filled with explosive vapors. The occupants of the minivan would have been injured from the collision but would have survived.
Prior to the car crash scene the brakes would fail within a short time due to fluid loss, which would have occurred in the city in stop and go traffic long before them getting to the winding road.
Noah gives Claire a copy of "The Iliad". Claire gasps that it's a first edition that must have cost a fortune. Noah jokes that it cost a buck at a garage sale. Claire, being a classics teacher, should know that "The Iliad" a 3,000-year-old ancient Greek poem attributed to Homer and was passed down as an oral tradition. The oldest and most complete manuscript dates from the 10th century. The "first edition" given to Claire is hardbound and written in English.
Claire says that Agamemnon killed Hector in Troy, but the truth is that Achilles killed him.
In the scene where the Challenger has no brakes and supposedly no clutch, the driver did not simply turn off the ignition. With the engine off, the car would decelerate, albeit not as rapidly as using the brakes. While this could be attributed to an inexperienced driver, the father was present and never suggested doing that. Additionally, even with a clutch failure the engine and transmission speed can be synchronized to downshift.