At the time of the film's release, the Army had already replaced its green camouflage Battle Dress Uniform with the pixel-gray Army Combat Uniform. Even if for some reason their unit hadn't gotten ACUs, the BDU is still worn improperly by every soldier in the film. They should have unit patches on the left shoulder, and an American flag on the right shoulder.
Captain Rhodes wears matching Captain's bars on the lapels of his uniform. Army officers only wear rank insignia on their right lapel. The left lapel is reserved for that officer's branch insignia, i.e. crossed rifles for Infantry, crossed sabers for Cavalry, crossed pistols for Military Police, etc.
CPL Cross ends a radio transmission with CPT Rhodes with "Over and out." "Over and out" is a contradiction. "Over" means "I am finished speaking, please reply." "Out" means "I am finished speaking, do not reply."
Private Crain did not attack the other survivors after he turned into a zombie. The explanation given (by Sarah) is that the zombies retain some portion of their former selves, and that he was a vegetarian, thus not interested in them for their meat. If we accept this explanation, then following the same logic, while walking in the woods not long after, he should be trying to eat the available vegetation (trees, flowers etc). However, he does not. Therefore, there is either an error in that he didn't eat plants when he would have done, or a plot hole in why he wasn't eating the survivors.
In the radio station right after Paul (Disc Jockey) turns into a Zombie and gets killed, Nina kneels down near a desk next to a computer. The computer is empty, it doesn't have any electronic components in the back like a video or network card. It's clearly a prop.
When Cpl Cross first arrives at the hospital with her mother there is a little boy being pushed in a wheelchair at the bottom left of the screen; despite being ill the actor is clearly smiling and looking straight at the camera.