Rick tried applying his old standards and morality to the new world, and as a result, found that he was constantly betrayed and screwed over by circumstance. Rick is now sweaty and desperate and amoral and awesome.
Lori sucked (Yeah, she came off as an annoying entitled cow no matter what. Her death was incredibly stupid (Her characters decisions made no sense there at all) but at least she's gone now). Lori is now dead. (Props to Andrew Lincoln for his acting at the end of the episode, very powerful).
T-Dog was underdeveloped, and seemed to be meant to be heading for something that never happened, frustratingly, since his character was then halfway between the fleshed out characters and the background ones. T-Dog is now dead, and died a hero, which I guess substitutes for him coming to nothing.
Carl was an annoying kid (I think a lot of the scorn heaped on him comes from not understanding small children that much). Carl has had to grow up and take responsibility, and is now hardcore.
Andrea was stupid, and then became stupid and pointlessly antagonistic (Like Shane, but without the sociopathic excuse). Andrea is now back to stupid.
I got annoyed during the second series where they'd constantly get stuck on stupid issues caused by characters being pointlessly antagonistic. Hershel wanting to keep the walkers was stupid. They couldn't survive even if they were cured.
Shane wanting to antagonise Hershel was stupid, Rick negotiating with Hershel was stupid.
Hershel not wanting them on his farm was stupid, and linked back to his other stupid.
I think they've done a good job at tightening up the pacing issues the second season had, and putting more of a clear arc in (Especially if you're ahead in the comics), while previous seasons didn't have good pacing, or a clear arc. If you look at the comics, I think it's because the source material up to the prison is mostly a travelogue of sorts, and most of what they focussed the series on was original, but trying to fit the canon.
The character focus has been what I always liked, and they've managed to patch up the characters who were annoying. Carl was annoying for me because he was only ever the cause of problems, he rarely got any characterisation. Lori was annoying because she took herself to be a leader with Rick, but instead backstabbed and exploited everyone. Rick I've always liked, and I like his overall descent into re-evaluating his moral standpoint.
I'd strongly disagree to anyone who'd call Rick a Mary Sue. He's an archetype of the conservative father figure, like Liam Neeson's Brian in Taken. However, Rick is a deconstruction of that. His straight-edge approach and his staunch opinions on morality cause problems when his views aren't pragmatic, his refusal to be pragmatic with threats (He gives Shane wayy too many chances. Watch Season 2, and count how many times Shane either tries to kill him or says he'd like to, and how often Rick lets him off. It's insane.), like Shane or the bandits. Over the course of the series, he reevaluates, killing Shane and refusing to trust the prisoners, but his group is too small to cover the prison, and as a result, the prison gets invaded and he loses his wife.
