Corrected entry: Both Captain Blackadder and Captain Darling make references to facetious conversations with Pope Gregory IX. Obviously they didn't speak to the pontiff, but it is not even a joke that way because Gregory IX was pope from 1227-1241; if they wanted the Pope reigning at the time of the Great War, they meant to say Benedict XV (1914-1922).
Corrected entry: While it is conceivable that Flashheart would be so lost as to be unaware of which side of the lines he crashed on, it is absurd that he would mistake a uniformed British officer for a German. The uniforms are completely different - they aren't even the same colour. 'Friend or foe' recognition was hammered into pilots at every stage of their training to prevent them accidentally bombing or strafing their own side.
Corrected entry: In the opening sequence, watch the members of the band who aren't in the main cast - there are at least two shots where one or more of the band are obviously smiling/laughing at what the main cast members are doing at the time (most noticeably is when Blackadder yells the "Eyes Right" command - there's a guy a short distance behind Blackadder who grins during the salute.
Corrected entry: Blackadder makes the joke, "I imagine he went to one of the great Universities, Oxford, Cambridge, Hull." This is probably around 1916, but Hull University didn't exist until 1927. We cannot put it down to the joke either, as he explains later the nurse failed to point out its quality, not its existence.
Corrected entry: Black Adder says that there are four verses to "God Save the King." There are actually five, and technically there are six. However, the final verse is very anti-Scottish (added after the Jacobite rebellion of 1745-46), and is very rarely seen and even more rarely performed.