Factual error: John Basilone was actually a Sergeant when he won the Medal of Honor at Guadalcanal, but is shown wearing the insignia of the higher rank of Platoon Sergeant. However, when his medal citation is read out it does give his correct rank (although senior sergeants in the US forces are commonly addressed simply as "sergeant", official citations give their full rank).
The Pacific (2010)
1 factual error in show generally
Starring: James Badge Dale, Jon Seda, Joseph Mazzello, Sebastian Bertoli
Factual error: On the map behind the colonel during the first scene, Iceland is labelled as being under Nazi control. This is incorrect, as the British were in control of the country during the whole of the war. (00:05:10)