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 Green Beret, but his shoulder patch is the 101st airborne, not Special Forces. Finally, he has six or seven hashtags on his right sleeve. Each hashtag is for 6 months of combat, meaning he's been over in Vietnam for at least three years.
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 mature bull Elk. Not typically found in the Appalachians.
Continuity mistake: During the long wedding scene, while Michael watches Linda on the dance floor, the level of the beer in his glass goes up and down several times.
Continuity mistake: When Nick is killed during the final Russian Roulette game, the gunshot wound on his bandana changes from the bottom to near the top between shots.
Continuity mistake: When the car vs. lorry race occurs near the beginning of the film, as the car pulls in front the left wing of the bumper clips the lorry and gets noticeably misshapen. Then the shot changes, the car spins round, comes to a halt, and the damage has gone (and remains so for the rest of the film). Possibly made worse by the fact they then make a big thing of Nick actually getting out the car and inspecting it for damage in a disbelieving fashion that anyone could have pulled it off without damaging it.
Continuity mistake: After Michael returns from Vietnam for the first time, he goes for a walk with Linda. As they start to pass in front of a store with a guy outside, Michael is shown fiddling with the collar of his coat. The shot changes, and though from their position and reaction of the guy outside it is supposed to be a direct continuation, Michael suddenly has his hands buried deep in the pockets of his coat.
Continuity mistake: In the scene where the boys are changing into all their hunting gear on the side of the road, keep an eye on Christopher Walken. In a wide shot, he's pulling on a dark green sweater. There's a quick shot of De Niro, then back to the wide shot, in which Walken is again pulling on the dark green sweater.
Visible crew/equipment: In the beginning of the film, when Linda is getting ready for her wedding, standing in front of the mirror at home, a boom mic is visible at the top of the mirror.