It's actually tough for me to call a character annoying, because most of the annoying things about certain characters are more about what is done to them rather than how they are portrayed.
Probably the best way to illustrate my point is Michael Burnham. For the first 3 seasons, it seems even when she did the wrong thing, she was somehow right for doing it. And it was constant. We saw some of our captains do some questionable things in the past: Kirk giving the Hill People rifles to have a balance of power, or Picard allowing the Boraalans to die, or Sisko poisoning the Maquis world, or Janeway obsessing over Ransom, or Archer stealing the warp coil. But it wasn't a constant thing for each of them. Those scenarios, while sometimes controversial, were exceptions in their time of command. With Burnham, it seemed to be the rule, not the exception.
In season 4, pretty much every member of the crew, at various points, were acting like they needed to pat her on the back or were saying stuff like "I'm with you, fully". I'm not saying that a captain shouldn't get positive reinforcement now and then, but she got more this season than ALL the previous captains of TOS, TNG, DS9, VGR, and ENT.
COMBINED! I feel that when you have to go to that extreme of having so many of the crew say those words, it undermines her in a way that makes it look like she didn't really earn the center seat. You want me to believe she earned the respect and loyalty of the crew? Do it with actions, not corny or overly saccharine dialogue. Janeway may have come across as a cult leader, but at least the crew
showed us they were behind her with actions.
I will say Burnham herself has been written better this season, but it's the surrounding things I stated above that undermines her captaincy.
Characters that started a bit annoying but got better:
- Wesley Crusher - not a controversial choice.
- Julian Bashir - seriously dude, take a hint and leave Dax alone.
- Neelix - they deliberately wrote him to be annoying to have other characters react.
Characters I liked at first, but then got annoying later:
- Jonathan Archer - it's weird to say that Scott Bakula was maybe miscast, but he maybe was.
- T'Pol & Trip Tucker - but only in scenes involving each other in some way.
Characters that could be great or annoying depending on the episode:
- The Doctor - one of my favourite and least favourite Voyager characters.
(Not an exhaustive list!)
I don't know if I was annoyed by Gray, though I was a bit bored during his scenes because of how isolated they were from the rest of the series and how little anyone got to do in them. He was perhaps the least fun imaginary friend I've ever seen on TV.
BORING! THAT is what I feel about Gray's character! I was looking for the right word to describe what I felt, and you nailed it.
Regarding T'Pol/Trip, I agree. It's one of the few things that I didn't like about ENYERPRISE, mostly season 3 and 4 interactions. The whole 'will they, won't they' is a tired cliche, and makes T'Pol look especially bad because she's much older than him.