Factual error: The boys go deer hunting somewhere in the Appalachians, but the geology is all wrong. That scene is in North Cascades National Park in Washington State. In addition, the "deer" they are hunting is a Red Stag. Not typically found in the Appalachians.
Factual error: When Michael Vronsky gets back from his tour he has a full grown beard. The only branch of the service that allows a beard is the Navy, and he was an Army Green Beret. The beard would only have been tolerated if Mike was either not in his Class A uniform or actively performing on a mission, neither of which are the case here. In addition, he's wearing a Black Beret, but his left shoulder patch is the 101st airborne, not Special Forces. Finally, he has six or seven hash marks on his right sleeve. Each hashtag is for 3 years of active duty service.
Factual error: Back from Viet Nam, De Niro is wearing a green beret and he has a 101st Airborne Division patch on the left shoulder of his dress greens. It should be a Special Forces patch.
Factual error: When Mike is hunting after his return he switches from left hand shooting to right hand and his rifle also switches the bolt on the right to the bolt on the left.