Factual error: Baldrick becomes Blackadder's navigator. The problem is, WWI aircraft did not carry navigators; they carried either only a pilot, or a pilot and an observer, and observers were officers. (00:15:30)
Revealing mistake: When the Baron punches Baldrick into the cell wall, it wobbles. (00:17:20)
Continuity mistake: When Blackadder's plane is shot, we see the bullets hit the side. In the next shot of the plane, not only is the side intact, but fuel is coming out of the bottom.
Other mistake: When we first see the plane that Blackadder and Baldrick are flying, the machine gun on top of it is firing. There are 3 mistakes here. 1) We don't hear the gun fire. Cannot be argued by the plane drowning it out, as we later hear the Red Baron's gun firing. 2) In the next shot, the gun has stopped firing. 3) The fact the gun is firing is ignored by Blackadder and Baldrick. They are too busy on keeping the plane level - the whole flying scene was obviously archive footage of WWI planes flying.
Suggested correction: OK a few points. 1. The baron and Blackadder are flying different kinds of plane. One could be louder than the other. 2. Gunners have to stop occasionally. So the gun stopping isn't a mistake. 3. We don't know for definite if they are ignoring the gun. This is speculation at best.
Continuity mistake: When Flasheart hits Edmund with the gun, he swings his arm to the right, but Edmund falls to the left.
