Offensively, I only see 2 positions that really need to be fixed.
WR-Franchise Welker with the intent to sign him to a multi year deal, re-sign Branch cheap, draft a WR like Kendall Wright or Michael Floyd in the 1st round. Let them compete to see who is the #2 or the #3. You'd hope the kid wins out and Branch's playing time/role can be scaled back a bit but if not, you've got plenty of weapons.
C-Draft Peter Konz in the 1st round and re-sign Connolly to compete for the starting C position or provide very solid depth.
Defensively:
Edge Rusher (4-3 DE, 3-4 OLB)-Make a huge push for Mario Williams. With Brady having a 3-5 year likely window left (and perhaps a similar one for Belichick?), it's time to get aggressive and bold. Don't be scared off by how the Adalius signing ended, people forget how good Adalius was in '07. That would've been a hell of a signing if Adalius were 27 like Mario is. Adalius just got old on our watch and for some reason, went from the guy making humble pie t-shirts to a cancer in the locker room. Mario's the scheme versatile, in his prime defensive difference maker that rarely becomes available. Jump on this rare circumstance.
I'd re-sign either Carter or Anderson to pair up on the edge with Mario. Carter is probably more likely to come at a reasonable price due to age/injury/wanting to win a title at the end of his career. But if you could keep Anderson at a fairly cheap price, I'd love to do so. He's got a lot of talent, I just would fear giving a guy who has been as inconsistent as him too much $$$.
Defensive back-I don't think it makes a huge difference whether we draft/sign a corner or a safety considering the versatility McCourty showed this year and the fact I think that Ras-I Dowling has that same kind of ability to switch to FS. I just want another talented defensive back to add to the mix considering that while there's some talent back there, it's got issues too.
McCourty had the horrible sophomore slump, Sterling Moore flashed a lot down the stretch but still has a lot to prove, Dowling has a lot to prove health wise as well as on the field. So while based on talent, I could see something like McCourty returning to form, Dowling converting to safety successfully and Arrington and Moore being good enough #2 and #3 corners, I think it's asking a lot to go right and we need to add more talent back there.
The rest of the holes you are talking about are minor depth issues. Add a late round RB to replace Benjarvus in draft, some additional DL depth to go with the kids who flashed like Love/Deaderick as well as a returning kid like Pryor, etc.
A WR, a C, a DE and a DB while re-signing some of our own guys are the big holes I see.