Continuity mistake: When Blackadder and the other soldiers are about to go "over the top", you can see two other soldiers standing behind Darling. They are presumably in the upper part of the trench. When Blackadder blows his whistle, you see all the soldiers climb onto their ladders and then start to rush over, side-by-side. In the next shot, when we see the soldiers emerging from the trench in slow motion, the other two soldiers are still back in the trench waiting for Darling to climb out before they move, as the two shots were filmed in two different studios.
Continuity mistake: When Blackadder, Baldrick and George are out in the no man's land, Blackadder screams and Baldrick asks why. Blackadder answers he put his elbow in a blob of ice cream while looking at Baldrick. When it cuts he is looking straight forward instead.
Visible crew/equipment: During the general's speech about how Blackadder is the person to organise a concert party, look at the entrance to the trench. In one shot you can see a crew member moving a giant cloth. You see mostly the movement, but you can catch a glimpse of the crew member's face.
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.