hate to tell you this, I seen a website written by another historian who wrote down the events from the show and what really happened. Each Episode had about half a dozen up to a dozen mistakes.
Example:
* At the beginning of the ninth episode, "Why We Fight", the date says April 11, 1945 as the episode opens with the paratroopers overlooking German civilians cleaning up their streets. At the end of the episode, the show returns to this scene, at which point Captain Nixon tells the others that Hitler had killed himself. However Hitler did not kill himself until April 30, 1945. Nixon wasn't told hitler committed suicide until May 3rd, Winters knew but said it could be speculations or rumors.
* At the end of the final episode, "Points," it is stated that Technician Fifth Class Joseph Liebgott became a San Francisco taxi driver after the war, but most accounts, including that of his son, state that Joseph Liebgott in fact became a barber after returning home from the war.
bill guarnere said this on a youtube video, nobody actually knew what he did, but during one of the meetings in 1980s he said to of been a barber.
* In the final episode, "Points," Major Winters accepts the surrender of a German Colonel, who offers him an ornate Luger pistol. In the scene, Winters tells him to keep his sidearm, but in the Bonus Features DVD, the real Winters recalls the incident and shows the pistol (a Walther PP) he accepted. In Ambrose's book of the same title, he describes how when Winters examined the firearm, he found it had never been fired, and he hasn't fired it since. He shows this firearm in the HBO documentary We Stand Alone Together. Also in book Beyond Band of Brothers : The war memoirs of Major Dick Winters written by Cole. C. Kingseed with Major Dick Winters it is said that the pistol was accepted but the rank of the German soldier was a Major not Colonel.
These are just the beginning, I haven't found the website - but the historian had a ton of information on the 501st, compares the show to ambrose's book and found quite a few errors in it.
There is a difference between minor details, such as the exact date of Nixon informing the troops of Hitler's death (which could indeed be a representation of Nixon passing along an unsubstantiated rumor, those things happen in war), or what job one of the men took after the war, or the rank and type of firearm carried by a surrendering officer, and what actually happened in a battle, such as a tank commander driving straight into a hidden enemy tank's kill zone, despite being warned.
No one, myself included, said "Band of Brothers" was a perfectly correct documentary. No such thing exists, no documentary is perfectly accurate. The point is, "Band of Brothers" is not rife with major glaring inaccuracies.