Factual error: All through the movie Pfc. Garlick is shown trying to turn the key on a jeep that is already running. The reason that this is a mistake is that tactical vehicles (jeeps) do not have ignition keys they have a starter button. So if you want to keep someone from stealing your jeep you padlock the steering wheel.
Continuity mistake: Garlick finds Cronauer sitting at a table with a couple of new friends in a local eatery and stands next to the DJ to tell him he has been reinstated to his job. At one point Cronauer grabs a piece of green salad with his chopsticks and puts it to his mouth and in the next shot from behind, it is the strands of white noodles that can be seen dangling from his lips.
Other mistake: In the scene in the Jeep when Garlick announces to the passing troops that Cronauer is in their midsts and Adrian does his riff, after the convoy starts moving again, more than a dozen trucks go by with all the troops grinning broadly and giving Cronauer "kudos," even though the majority of them couldn't possibly have heard or seen his Jeep "performance," and wouldn't even know who he was.
Continuity mistake: Before Adrian Cronauer does his first broadcast on the air, he puts on headphones with a side cord on his right. After a quick cut to another man in a booth, the side cord has moved to the left, and just before the broadcast begins, the cord has moved back to its original position.