Hermann Fegelein was executed by gunshot, not by hanging.
At the beginning of the movie, the narrator enters Hitler's flooded underground bunker shortly after the German surrender in 1945. He wears the uniform of a U.S. Army captain, and says he is on assignment from Newsweek magazine. However, civilian publishing companies did not employ military officers as correspondents. But the military did enlist journalists. To maintain order, war correspondents were given temporary commissions in the military. There was an understanding that in exchange for their compliance with military direction they would receive access to military operations/facilities and as much freedom to report as possible. By and large this worked well with the journalists of the era.
Bormann refers to Gen. Patton's 3rd Division as crossing the Rhine. Patton commanded Third Army, a fact which the German staff would be all too aware of.
In the film, the stairway between the upper bunker (vorbunker) and the lower bunker (fuhrerbunker) is shown as spiral. All witnesses to the final days in the bunkers say that it was a normal staircase with right angles.
The term "Jerry Can" for the German fuel canisters is strictly a British and American term. The Germans referred to them as "Wermacht-Einheitkanister" (Wermacht Unit Canister).
At the very end of the movie, the SS man/switchboard operator, Misch is seen talking to mechanic Hentschel while preparing to flee "The Bunker". The rifle Misch has shouldered is a Russian Mosin Nagant; he would have been carrying the German Mauser of which plenty would have been available with all the wounded in the proximity. It's unlikely anyone would have taken a Russian weapon down into Hitler's Bunker.
Apart from Anthony Hopkins (Adolf Hitler) - all the men's hair is styled in the longer, more casual look of 1980, unlike the shorter military look of 1945.