First off, I just have to get this out of the way: DRAFT! I love the NFL Draft. I do love it dearly. It's up there with Bacon and Latin. And also Bacon. I don't want to talk only about the draft...
...so let's talk about the draft. Specifically as it relates to the Miami Dolphins. The most obvious need for these guys is the QB position. In case you have ignored every Mock Draft ever written, the Dolphins are expected to take Ryan Tannehill, the QB from Texas A&M, with the eighth pick. This seems like a bit of a reach to me, but eh, they have some coaching connections. Also, the pretty much just swapped QBs Chad Henne and David Garrard in Free Agency moves. Add in Matt Moore, and you can understand the impulse to take Mr. Tannehill.
Outside of QB, it seems like the Dolphins actually have quite a few needs going into the draft. I have seen people making arguments for needs at the LB corps (gotta get more pass rush!) and the Secondary (which actually makes a ton of sense. See: Tom Brady). Along similar lines as the QB swap, the Dolphins lost S Yeremiah Bell in Free Agency but signed CB/S Richard Marshall. Also, you can't cross of a potential need at WR, especially if Tannehill is going to be the guy next year. Get some offensive weapons on that team. WR Brandon Marshall is gone now, and while I just saw him described as a "headache," they are going to want to replicate his production somehow.
One universal need, it seems in most evaluations of the team, is at o-line. The team lost both OT Vernon Carey and OG Marc Colombo in Free Agency. I would imagine that they are going to try and patch up some holes on the o-line through the draft. Even just o-line depth would go a long way with this team.