1. Wide Receiver: Everyone knows the Wes Welker debacle, and Brandon Lloyd was also cut. Amendola was brought in, but he's injured so often it's hard to count on him. The only other targets on the roster are two more injury prone players; Julian Edelman and Donald Jones. New England could easily double up on wideouts early in the draft. I find it hard to believe they pass on one in round one especially.
2. Cornerback: Talib will stay as the #1 corner and Arrington can man the slot, but someone else is needed to start across from Talib. Dennard would be a solid option, but his legal situation is dicey and he might not even be playing football. A cornerback will probably be taken on the first two days of the draft, as early as round one.
3. Defensive Tackle: Defensive Tackle is the only other position New England could conceivably take in round one. Wilfork is obviously a star, but they need another strong presence working next to him. The DT class is extremely deep and talented, so a quality starter could be found on the first two days of the draft. However, the need is not dire at this position, so they might not worry about trying to upgrade.
4. Defensive End: The Patriots have a few people to plug in across from Jones, but no one that has proven to be a consistant impact player. There is a very deep class of pass rushers this year, so they may opt to take one with a mid to late round pick and hope he develops into a starter.
5. Offensive Line Depth: New England has a solid offensive line at every position, but lost some quality depth through free agency this off season. They could take someone with a late pick to help replenish some of that depth if they find some value.