Considering the comments Michael Gove made about Blackadder Goes Forth in OTL, they would've arrested Atkinson as soon as someone saw a script. You can't let the public see unpatriotic tosh like that.I can't imagine Blackadder Goes Forth being made in this environment. The military leaders would not look kindly on the urine being extracted from the gallant actions and the brave soldiers of The Great War.
Same probably goes for It Ain't Half Hot Mum and Dad's Army unless they are written with a slightly more serious tone or greater respect in each episodes outcome.
I can imagine Dad's Army being totally different to OTL if it ever got made. No more rivalry between Mainwaring and Hodges, Godfrey's storyline about being a pacifist would be gone and Walkers black market exploits would be gone too. There'd be more episodes about capturing Germans too. I doubt it would last more than one series.