Remaining needs: CB, TE, OL, NT
The Colts have the first overall pick in the draft, so they would get a free pass, but they've dropped so many players it's criminal.
Of course, their biggest hole is at quarterback, but that'll be fixed with Andrew Luck. His biggest problem in his rookie year will be a lack of protection. Assuming Ben Ijalana is the right tackle of the future, the Colts need to find a center and two guards to get a decent line.
With the departure of Dallas Clark, they'll also need a new tight end.
On defense, since they're switching schemes, they'll need all kinds of stuff, but the biggest problem is securing a nose tackle. Nose tackles are hard to come by, so I wouldn't be surprised to see the Colts take Alameda Ta'amu with the the second pick of the second round.
Realistically, the Colts could use upgrades nearly everywhere. Minus Andrew Luck and whoever they snag in the second round, I expect the Colts to be just plain terrible next year.