Archie's wife is presented as cold, nagging and uncaring, and Archie is one of the viewpoint characters, so we're meant to root for him. However:
He is having an affair. Comedic situations aside, it's he who betrays her trust;
Is the wife really that bad to him because *she* doesn't care? When Archie is kissing her, she says "that's so unlike you" and she seems happy, even delighted. It's not that strange that she wouldn't be very affectionate if she never seems to be on the receiving end of attention. When she thinks she got a gift from him, her reaction is genuinely thankful;
And the big one: she overhears Otto claiming Archie robbed his own house and is "porking" Wanda. She seems to give Archie the benefit of the doubt and not jump to conclusions. She only threatens divorce after Archie confirms her suspicions *and* humiliates her in public by calling Wanda "darling".
Considering all these, who is the villain in the situation?
Cool Car: Archie's Jaguar XJ12 H.E. (5.3 litre V12, the most expensive model after the Daimler Double Six)
Comedy Ghetto: Kevin Kline's Oscar was a rare win for a comedic role.
Crosses the Line Twice: Ken's repeated attempts to kill an old lady, accidentally killing her dogs in the process (much to his despair, being an animal lover).
DVD extras show that another running gag was dropped completely wherein Otto practices his marksmanship whenever he hears a cat by shooting its tail off (you see him shoot off screen then hear a yowl but later see him arranging the tails like flowers in a vase). It was dropped because combined with all the cruelty to dogs as well it really was crossing too many lines.
Michael Palin said that the film-makers filmed the reveal of the sadly flattened dog with guts visibly squashed out of it, which upset a test audience. They decided that the plain flattened dog was comically shocking while avoiding being gruesomely realistic.
Ensemble Darkhorse: Otto is an absolute blast to behold, thanks to Kevin Kline's fantastic scenery chewing and the wonderfully absurd nature of his jingoism. As mentioned above, the character was so great that it netted Kline an Academy Award for Best Supporting Actor.
There's also a great deal of love for Michael Palin's Ken, which won him a Best Supporting Actor prize from BAFTA.