Continuity mistake: Just after Knoll has been beaten up we see Elwood sitting next to him. As Elwood switches on the light, we see that the left side of Knoll's face is covered in blood. After Elwood applies the bandage, the blood on his face has changed with much less blood on the left side. The blood was never wiped off.
Continuity mistake: Why do Elwood and Garcia drive one truck into the nuke base with the weapons, if there were 3 vehicles and 3 people to drive them? That would mean either the Hummer that Stoney drove or either of the trucks was abandoned in the forest. It was most likely that both trucks had similar cargo, even then, why were the not escorted due to the nature of the cargo?
Continuity mistake: Watch the eye-patch of the soldier as they are around the campfire. It switches eyes. Easy to spot.
Revealing mistake: In the last shot of Elwood machine gunning his Mercedes, he's run out of ammo - there's no belt left.
Deliberate mistake: The tanks used in the film are German "Leopards", never used by the US army.
Visible crew/equipment: When the tank drives through the town and mangles the Beetle, you can see at the back of the car where they pinned and tied it to the ground so that the tank would go over it.