The Destroyer (or battleship) that's how confusing this is,show sailors in dress uniforms not dungarees and helmets.Not a Navy officer in sight...
Regular German army soldiers did not wear Swastika armbands.
At the beginning of the movie, a sailor stops to salute the major. Sailors do not salute inboard a ship unless they are reporting to an officer on watch or reporting to the CO at Captain's Mast for non-judicial punishment (UCMJ Article 15).
D-Day show the American troops attacking the Germans in the sunshine. The weather was overcast on D Day.
Rank was warn on the shoulder lapel not on helmets in the US Army during WW II. Standing out as a commanding officer would make them the main target of the enemy. Officers tried to blend in as much as possible.
Ranger patches were sewn on, but one of the medics patches isn't totally attached to his shoulder.
When the rangers first assault the beach, there are already ropes draped along the cliffs that they are assaulting.
One of the soldiers is ordered to use his 'bar", which is actually called a B.A.R. (Browning Automatic Rifle). Also, his (fake) BAR obviously has a capped end on his "rifle barrel".
A red Massey-Ferguson TE35 tractor shown in the fighting scenes after 1 hour. The tractor model were in production first in 1956 to replace TE20 introduced in 1946 (grey)
And the "German" trucks in the same scenes are American Ford trucks from late 1930s.