Continuity mistake: During the briefing Alexei Vostrikov was receiving from the Generals, he has three stars on his shoulders, but for the most of the rest of the movie he only has two stars on his shoulders.
Factual error: As the 1st Battalion, 7th Cavalry lifts off from LZ X-Ray at the end of the battle, it can be seen that there are no more American troops left at the battlefield. However, by the time 1/7 CAV left LZ X-Ray, it had been relieved by two full battalions (2/7 CAV and 1/5 CAV). There were around 700 American soldiers occupying LZ X-Ray by the time 1/7 CAV lifted off.
Revealing mistake: In the final fight scene in the desert between Broken Sword and Flying Snow, when the camera cuts to the wide shots of them standing there, looking at each other, you can see tire tracks in the sand. (01:24:30)
Factual error: One of the members of the orchestra is reading off sheet music held together by sticky tape, which is an anachronism.
Continuity mistake: When the priest is waving the handkerchief, the fabric changes from covered in blood to spotless.