Private Miller is chastised by Cobb for wearing a "presidential unit citation" even though the replacement soldier did not fight in Normandy to earn the award. This citation was not called the "presidential" citation until 1966, when the award was initiated in the 1940's it was called the "Distinguished Unit Citation".
When Pvt. David Kenyon Webster spots the road sign for Nuenen, he states: "Vincent Van Gogh was born in Nuenen!". Van Gogh was born in Zundert, although he did live in Nuenen for two years from 1883-1885.
The allied forces throw a rocket at the Dutch restaurant, leaving a huge hole in it. Still, they are forced to retreat. Afterwards, we see the victorious Germans in front of the restaurant with no sign of the previous damage.
During the German counterattack, Easy blows up a machine gun nest in a building marked "petite restaurant" with a bazooka, collapsing the wall. Later, in the shot that eventually shows Bull hiding in the culvert, we see the Germans maneuvering past the same building, now undamaged. This could not have been the opposite side of the building since it would mean the Germans had their backs to the retreating Americans.
At the 37 minute mark, Roy Cobb is squatting down, firing his Thompson over a short wall. The wall is hit by a shell and breaks apart as Cobb is firing a burst. The camera then immediately cuts to Cobb, who is now seated with his close to his chest.
When Sgt. Randleman crawls away from the damaged US tank which is chasing him, when the tank is seen from behind, two crew members are visible walking along the right side of the tank, partly hidden by some bushes.
(at around 33 mins) When Bull is crawling away from the burning tank, on shot of the rear of the tank reveals two crew members in white (one wearing a baseball cap) walking alongside to the right of the tank.
While retreating after the battle in Holland Lt. Nixon is struck in the helmet by a sniper's bullet, when in the actual war this occurred while the company was crossing a field and a machine gun opened fire. Nixon survived as portrayed in the movie.
Officers assigned (and qualified) to Airborne units worn their rank on the left side of their garrison cap and the "glider patch" on the right side. NCOs/Enlisted wore the glider patch on the left side. In Band of Brothers, everyone wore the glider patch on right side.
Buck Compton and Babe Heffron are playing a game of darts. To finish, Babe says he needs "double seven". He throws and apparently wins the game, but the arrow hits "treble seven", instead of double, indicating that he didn't win (yet).
(at around 30 mins) In the scene where the paratroopers are landing in Holland you see a paratrooper land and roll. Immediately after, Sgt. Denver 'Bull' Randleman runs in from the left and helps a paratrooper out of his chute, telling the trooper "Don't be sorry". During this scene, the shadow of a parachute in the background never moves or changes until the camera pans all the way to the right, when the cables release and the obviously suspended parachute and actor roll into the shot, simulating the landing.
During the jump scene Les Hashey has problems releasing the QRF on his harness after he lands. Sgt Randelman comes along and releases it for him and says "don't be sorry, grab your rifle, lets go". Les Hashey does exactly that but doesn't take the harness off his back, seemingly running off with his parachute still attached to him.
When Easy Company are parachuted into Holland, just after we see Pvt Hashey struggling with his harness, a paratrooper lands and rolls in the center of the screen. His parachute drops in a heap behind him, clearly indicating that he and his 'chute have been dropped from a platform, gantry or crane.