I think Katniss was completely serious when she voted for another Hunger Games. It's possible that she and Haymitch voted as they did because they really thought it would result in the fewest deaths (as opposed to Enobaria and possibly Johanna, who cast their votes for revenge), but I think Collins meant them to vote their true opinions rather than some strategy to distract Coin. It's certainly possible that the last Hunger Games didn't happen after Coin died, but I think Katniss intended them to.
I agree that there was a plot in there, and that Collins might have had more luck with it if she hadn't insisted on writing from Katniss's point of view. Philip Pullman, for example, has had a lot of luck with shifting his stories away from protagonists once they got boring -- but he needed a third person POV to do it. (For the record, though, I think the first book was a really striking example of first-person-present-tense writing -- I can't think of a book that did it better.)
Re: I thought it was awful.
I agree that there was a plot in there, and that Collins might have had more luck with it if she hadn't insisted on writing from Katniss's point of view. Philip Pullman, for example, has had a lot of luck with shifting his stories away from protagonists once they got boring -- but he needed a third person POV to do it. (For the record, though, I think the first book was a really striking example of first-person-present-tense writing -- I can't think of a book that did it better.)