Factual error: The U.S. Paratrooper uses his "clicker", and the German answers with a "double" click-click - click-click. The Paratrooper stands up, and the German soldier shoots twice with his Mauser K98 without pulling back the bolt between shots, which is impossible.
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Suggested correction: There could have been another German soldier present who fired as well.
Factual error: In the film, the mutiny occurs during the day, when Bligh allows a crewman to die of thirst. The actual mutiny occurred in the middle of the night, when Christian and several followers entered Bligh's cabin and awakened him.