Frankly we don't know much about the guy. I can't think of a single profile that was written about him since he became a Dolphins coach. In general, though, Parcells is known for hiring good people, but even more important than that he hires "his" people, so now and then you get a guy he likes but who is nevertheless a dunce as a coordinator or head coach (see: Groh, Al).
As a coach, though, it's hard to say what Edwards will be. But I think every Dolphin fan would agree that our linebacker play this season was extremely disappointing. They played slow, they didn't make plays, and now and then they made huge mental errors.
The coaches couldn't get Cameron Wake -- our best and most dynamic pass rusher -- to the point where he could be on the field on 2nd down pass/run situations, preferring to let an injured/substandard guy like Joey Porter, who's also lousy against the run, stay out there. As a result, we got our butts kicked on second down passing plays all season long.
Our safeties were 1 and 2 on the team in tackles. That should tell you something. The ILBs were consistently late getting over on seam routes to the tight ends, and that was when they weren't letting those same tight ends get open down the seam by biting on play action fakes.
So I'm not sure what I can tell you. From a scheme point of view, expect Edwards to focus on stopping the run to the point where they get murdered by the pass. Expect big, slow, plodding players. Expect a monomaniacal reliance on the steady and expected rather than the situational use of the dynamic but inconsistent.