In order:
OL - Every game with Kline out there is a tremendous risk (He did well against Ravens and Colts though). Upgrade to the interior OL is absolutely needed. Hopefully we get lucky and an immediate starter falls in via the draft, Stork keeps developing, and Connolly can be affordably kept.
DL - I will be fine if Ayers and Branch are resigned (Ayers' situation is harder). We can only hope Easly improves, but I still see a necessity for another player there, specially considering Wilfork's age. I'm fine standing pat at DT if Branch re-signs. I agree that Ayers is less likely to be affordable, and that we're dangerously short on edge rushers without him. That's how he came to be on the team in the first place.
RB - Only Blount, Gray and the rookie that was taken from Carolina are under contract. And Bolden. Although we were able to win it all without running plays all that much, I don't think we would have won without Vereen. The Redmond/Faulk/Woodhead/Vereen position is pretty crucial on the Pats.
LB depth - Mayo is a puzzling piece of Patriots offseason. Should we keep him and his big salary, even though our team didn't miss him? Still, I am not confident with any player that is behind Collins and Hightower in the roster. Mayo is quite valuable, although I recall that some years he used to come off the field in sub.
Safety - We only need to resign McCourty to be fine. Still, if that doesn't happen, i would be very afraid of having only Chung, T. Wilson and Harmon. McCourty to Harmon would be a major downgrade.
WR - Amendola got his s*** together and was trully clutch in the play offs. He is expensive though. Even if we were to retain him, I feel like there's room for improvement at this position (Edelman is the only one who would be borderline impossible to improve). If Dobson can get rid of whatever thing that has possessed him this season, I would already be very satisfied. I think Amendola can make more money elsewhere, more's the pity.