Offense Starters seemingly locked in unless surprise happens:
QB - yes
RB - yes
3dRB - yes
FB - yes
LT - yes
LG - yes
OC - not a first rounder in the draft
RG - no
RT - yes
TE - yes
WR1 - yes
WR2 - yes (?)
SlotWR - yes
So, on offense, the only immediate openings would be, perhaps:
OG
WR
OC
Are you recommending that the Patriots draft one of those positions in round 1?
Defense starters seemingly locked in unless surprise happens:
DE - yes
DE - yes
DT - yes
DT - yes
LB - yes
LB - yes
LB - ?
CB - Revis
CB - Browner
CB - Dennard
S - McCourty
S - no
So, on defense, the only immediate openings would be, perhaps
LB
S
Looking at positional needs and cross referencing them with draft availability, it would appear that, in all likelihood, this team's not drafting to fill holes at starting positions in the first round unless players surprisingly fall (S), the need is thought to be greater than most others believe/admit to (WR), players in waiting aren't ready despite the hopes of the team/fans (LB, S) Injury leads to necessity (DT) or the team drafts the position higher than it ever has (OG).
While it's possible that one of the above will be the case, I'm not sure you could get great odds for it.