For me there's a difference between characters who are annoying but well written in that regard and characters who are pointlessly annoying or badly written.
First, to get it out of the way, I do like Liara in ME1. However I do dislike her change in ME2 and I do get while others think she's pushed a bit too much.
Talking about pushing characters, there's Miranda. I feel that she is just as much pushed on me as Liara. She also has to go into the pointlessly annoying category for me. Smug, pointlessly bitchy and needlessly antagonising (her harassing Jack is a case of "too dumb to live"). Her sexualised depiction makes it worse - if I don't like her otherwise, butt-shots won't help, no. They make it worse. Oh, and at least according her LotSB dossier, she pretty into Cerberus' ideological bullsh*t as well.
Udina's a pretty annoying prick, but for ME1, a well done one. A Power-hungry, opportunistic career politician. He's a great "love to hate" character. The Dolores Umbridge of Mass Effect. For ME2, he has not much meaning (never choose him anyway) and by ME3, he's either insane or a case of wasted potential.
Foster Addison also makes it into closer consideration. Unpleasant and incompetent, but still another good "love to hate" character. I like to play Ryder continously exposing her fuck-ups in anticipation that she'll get finally replaced by someone more competent and more pleasant to work with.
Kai Leng. Pointlessly annoying and useless as a character. In order to spare myself some grief, I tend to view him as some play on cheating teenagers talking shit on the multiplayer of FPS games.
But the priiize goes to... no, not Jacob. It goes to The Illusive Man. Most dialogues with him are either instances of frustrating railroading, disruption of Shepard's character agency, incessant fanatic blathering, vague insinuations that my Shepard has to believe because the plot says so, plus pointless circular discussion that lead nowhere and are actively wasting precious time by ME3 (Thessia and Cronos station). He's less of a character and more of plot device, author self insert or a type of the dreaded game master NPC, able to pull anything he likes out of his butt. Or some kind of villain sue.
Ah, /endrant