In "Currahee", Robert Strayer is (correctly) wearing the rank
insignia of a major when Easy Company is celebrating its paratrooper qualification. Strayer was promoted to lieutenant colonel in January or February of 1943, and Winters refers to him as such during his explanation to Sobel about the latrine inspection incident. On D-Day (in episode 2) just prior to the attack on the 105mm guns at Brecourt Manor, Winters and another officer refer to Strayer as a major. He had been an LTC long enough (16 or 17 months) to rule out a slip of the tongue, especially by two different officers.
In, "Points", when Easy Company first enters Berchtesgaden, the first shot showing the white flags, on the left, in a first-floor window, you can see someone with a handycam/miniDV shooting the actual film crew and cast.
When the 101st Airborne was sent into Belgium just before the
Battle of the Bulge they were ordered to remove the Screaming Eagle patch from their uniforms, so the Germans would not know they were facing an elite division. It was only after the battle when they moved into Hagenau that they were able to wear the patches again.
In the episode where Easy is rescuing the British soldiers, Bull Randelman is seen in the extreme foreground. He is in a boat paddling along with the rest of the soldiers, but he does not have a paddle in his hands.