I mean more in terms of characters, rather than actual annoying writing. Like imagine the whole point of a character is annoying, but then they turn around and actually end up being badass so you tollerate them. that sorta thing. There's also the thing of a 'returning gag' and I'm a bit cautious about how often is too often, especially when said running gag is something that's infamous for annoying readers. I don't know if it helps to have the characters become increasingly self aware of the gag itself. Sympathy points only go so far with this kind of thing.
I guess the trick would be to make sure the reader understands that the character is supposed to be annoying. Problem is that this is kinda subjective. There are characters I really liked that my brother absolutely couldn't stand, specifically because they annoyed him. We have different tastes and tolerances for this sort of thing, see. One readers "endearing" may be another's "obnoxious." Heck, I have a strong preference for haughty, arrogant characters with potential for hidden virtues and character growth, whereas other people often just view them as stuck-up bullies. Generally, the safest bet is probably to make them annoying to other characters, rather than trying to annoy the reader. That makes the annoyance an informed quality that one doesn't necessarily have to agree with. Also, positioning them in roles where they can get away with it probably helps. For example, nobody expects minor antagonists to be very likable. Then you can reveal their better sides and phase out the antagonism. I think pacing and timing is probably important for running gags. You want to space them out so that the previous one isn't fresh in the mind of the reader, and maybe try to subvert their expectations once the pattern has been established. Let's say you have three gags with about the same amount of story between them, and then quite a bit later when the reader thinks you've abandoned the gag, you hit them with a fourth one. Humor often fails when it becomes predictable. Also, don't just repeat the same gag. Try to step it up and put a new twist on it each time, be clever about it. Finally, don't force the jokes, try to make them seem spontaneous and natural. This is especially tricky when it comes to running gags, obviously, but nobody said comedy is supposed to be easy.
With this issue I always refer back to A Confederacy of Dunces, in which the primary protagonist is an annoying self-centered jerk, who never really changes. He's easy to dislike, even be appalled by, but there's also a desire (at least for me) to keep reading, sort of like rubber-necking an accident on the freeway; one can't help oneself.
In Michael Moorcock's novel Byzantium Endures (set during the Russian civil war) the narrator is an over-the-top anti-Semite who is also probably of Jewish descent and, from the very start, in fierce denial of it. The running gag of the book is various people assuming he's Jewish and his knee-jerk refutation of it. I thought it was funny but some people find it a bit tiresome.
Don't annoy the reader is a cardinal rule. Every word in the story is draining some of their life-force back into the stream of collective verbal consciousness, and they do expect to be entertained in return for this. On top of that these crazy individuals have even paid money! If a character is thought of as being annoying to other characters - I think this is a mistake, because characters don't exist to each other at all - they only exist to the reader. Roald Dahl's Mr & Mrs Twit would be annoying if we lived next door to them. Possibly even dangerous. They are hugely and continually annoying to each other. But they are not annoying characters - the reader's loyalty even switches back and forth between them because the writing evokes a sense of gleeful sadism. Is the OP related to the WIP workshop entry at https://www.writingforums.org/threads/hound-and-fox-prologue-scene.170845/ ? I didn't get the sense that any of the characters there were annoying - yet - but the security guard might be an example of something similar. They might throw difficult questions at the MC and act as an obstructor. Potentially they could be the antagonist or gatekeeper and do that all the way through the book, so long as it never gets old or repetitive. The MC is rejected, goes away and develops a bit, and returns, and the security guard tests in tricky ways whether their development is genuine, or maybe he moves the goalposts. This is different from Mr & Mrs Twit because it pushes more of, or all of, the interest value onto the MC. But it can be done that way. "Computer says no" could be made to work as an antagonist. There aren't many words to infer anything from in the OP... but I get the sense this is really about can a minor antagonist have a character arc where they develop into a supporter. Certainly they can. So long as they don't annoy the reader. With running gags I think the test is to read enough of the story out to people and see if they chuckle. I take this to be running gags that aren't funny in their own right (or otherwise the question wouldn't arise). Personally I would be inclined to avoid that approach that since we never know how much attention the reader has been paying. I believe whatever page the reader opens the book at, it should be entertaining - and anything in the story that relies on previous passages in previous chapters for it to entertain at all is letting the reader down. (Mysteriously, at the same time, every word of the story should enhance the meaning of every other word.) Just to test, I've picked up The Worm Ouroboros, which is a fantasy story I haven't read before, and which is from 1926 so might be convoluted and unclear. [QUOTE:E.R.Eddison, The Worm Ouroboros, 3rd printing 1962] precis of page 201: someone called Lord Juss is crossing the Bhavinan river. He's taking the omens. Lord Brandoch Daha asks if they're walking or swimming or flying. He doesn't fancy swimming with lots of armour and weapons. Their language is super-flowery medieval, which is a hoot. Juss says the crocodiles will carry them over - he's been buttering them up for just such an occasion. Their friend Mivarsh says a wise woman told him his doom was to be eaten by a crocodile, but he'll give it a go. They whistle for the crocodile. The first two go across. Mivarsh sits right at the end of its tail, praying to his gods, with his anti-reptile charms ready. They get across the river. They thank the crocodile. And that's the end of the page. [/QUOTE] Great stuff. I feel sufficiently entertained to turn back to p1, but also reasonably tempted to turn on to p.202. Running gags I think need to do the same.
Like Gump, right? He's irritating in his naivete, but always seems to conquer. People around him eventually realize it and draw strength from his simplemindedness. I'll bet when he opened fire during that Vietnam scene, every round took out at enemy. He left a swath of death and destruction.
I dislike when a story has an annoying character that turned into the hero in the end. So the dingus who was a jerk the whole time saves the day and doesn't learn a single thing and gets a pass because they were the hero? Nope.