Since the Kimi ni Todoke manga is still running, and the anime ended in 2011, it's safe to assume that the anime didn't adapt everything. However, I know that a lot of it was adapted reasonably faithfully, and I'd rather avoid rereading things which were part of the anime.
What manga chapter corresponds to the end of the second season of the anime? Also, are there any story arcs which were omitted from the anime up to that point?