To satisfy my curiosity, of you don't mind, which bits irk you. As an historian myself I have my own thoughts, but keen to hear yours.
I'm not hugely articulate in writing. However, I do think that Elton and Curtis were naïve in their writing, probably written without much historiographical consideration. To the average comedy fan, this won't matter. However, many people do not realise how many of their initial opinions on subject such as WWI stem from television shows like Blackadder. It annoys me when writers get so many important and tragic events wrong, U-571 and The Patriot being recent Hollywood examples (which, in fairness, fooled few).
As you probably know, many academics are critical of the Blackadderisation of WWI which has given a generation of people an a collection of opinions on WWI which aren't true (in places). I'm not in agreeing with Gove who essentially wanted Goes Forth banished but it does have worth as a starting block for a more comprehensive study/discussion.
And as a comedy, I fully agree with A Gent Orange.