Here are what I think our needs are in order of relative need with some explanations:

DT (3 tech) - We need a play-making DT. We haven't had one in forever.
MLB - Fox has said we need to get faster, I think this starts with a true, every down MLB. I don't know if Mays is a starter.
RT  - We didn't re-sign Ryan Harris. I think we draft a stout RT.
DT (1 tech) (We only have 1 DT on the roster with no CBA in sight) Vickerson can play this position, but we need some young bodies as well.
SLB - Going with the faster theme, I don't think Haggan is a good fit for this defense. I think he gets moved/cut. I'm not sure Woodyard can play SLB. There are a few decent SLB prospects in the draft that can fit the scheme.
SS - Dawkins is old and slow. I think he's done. I'm not sure Bruton or McBath can play consistently. We need more.
FS - Hill is serviceable for the time being, but we need depth and youth at the position.
RB - Obviously, Fox loves him some RB's.
TE - Blocking or pass-catching, we need more bodies.

I think we are set at QB (I'm not playing)/C/G/WR and CB. But, we have a lot of needs and not enough draft picks. The lack of a CBA sucks.