No, not really. If that's all you got then it's plainly obvious you were trying to find fault with him, or didn't initially like him and decided to ignore any progression he makes.
He's just a plainly uninteresting character that isn't well differentiated from other shounen protagonists. He's a nice guy who wants to protect his friends. That's largely the extent of his character. He doesn't have faults. He doesn't have quirks.
Kirito is Gary Stu. All the girls with screen time in the show like him. He's a chosen one (having his special skill). The villain of the second part is after his girl. He's pretty much faultless. He wins every (or nearly? I can't remember) fight he's in, and wins them mostly all by himself. He's the best at most everything he does to the point of absurdity. Remember how he beat the best player in ALO with some of the best equipment in the game literally one day after picking it up?
He's an obvious, boring vicarious doll for male viewers.
An antagonist has no existence outside of being antagonist?
Yes. He's comically evil. His plan makes no sense outside of providing Kirito something to struggle against so the story is interesting. Taking over people's minds with nerv gear? A fairly ridiculous thing in itself and a fairly generic take over the world plan, but let's have the stand. It's incredibly convenient that Asuna is both Kirito's GF and the object of his desire, but that too can stand. Why the **** is he in the videogame? Because the story wants a cool fight scene. It's ridiculous.
If you're "rules of the game stop applying" part is referring to the last in game 'fight' in the fairy dance arc, I agree with you. That part was sh*t as far as I'm concerned. Everything else was consistent as far as I remember though.
I had forgotten about that. The most obvious one is the ending of the first cour. Asuna dies in game, which should mean she dies in real life, but she doesn't. Kirito wills himself to win the fight, in seeming defiance of any game mechanics.
There are many other minor details. There are a few reasons for switching in fights, such as taking advantage of cool downs and confusing enemy ai, these are largely discarded and not brought up again along with Kirito mostly soloing encounters.
I'm certain you remember the details far better than I do, but honestly it's not any one thing, but the summation of all the various faults and lack of redeeming content. SAO, as presented as an anime, has terrible writing. It's got a nice setup, but it falls flat. Animation, good. Visual character designs, above average. Music, enjoyable. Edited, Jun 21st 2013 5:36am by Allegory