How historically accurate is it? What was the controversy behind it?
This question upon further examination has been answered before.
Please refer to this thread:
As for my own musing and mini-answer.
Here is a quote directly from Oliver Stone.
"Vietnam was really visceral, and I had come from a cerebral existence: study... working with a pen and paper, with ideas. I came back really visceral. And I think the camera is so much more ... that's your interpreter, as opposed to a pen." —Oliver Stone
Source: Salewicz, Chris (1999-07-22) [1997]. Oliver Stone: The Making of His Movies (New Ed edition ed.). UK: Orion Publishing Group. ISBN 0-7528-1820-1.
This is based upon his own experiences as a U.S. infantryman in Vietnam. As far as historically accurate I think you have to keep that mindset. That the events and storyline mimic events which happened to stone. Of course their is the imprint of Hollywood on the film, but there are real elements to this story.