Plot hole: Aside from the fact that you can't have a semi-automatic rifle delivered to your doorstep (except to an authorized dealer), there's also the fact that the weapon apparently was shipped with a full magazine. This is ridiculous. All the boy did was take the mag from the box to the gun and it started firing right away. One can assume they already had the ammo and filled the mag inside the house. This is countered by the fact that when he takes the mag out of the box, it is empty. Freeze-frame confirms there is not a single cartridge in the magazine before it is inserted into the weapon.
Continuity mistake: Early in the movie, just before John is seen leaving the school and passing the gun-toting students for the first time, John is shown briefly coaxing a dog into a little high-jumping trick. Much later, when the same scene is viewed from the gun-toters perspective, the dog doesn't do the trick.
Continuity mistake: Due to the different perspective during the whole day, there are some inconsistencies in the events during the day, for example when John leaves school early on in the movie it is a dry day. But later on, when shown from a different perspective it is very wet as he leaves.