I think you start at the top and work your way down. The organization didn't spend like the 49ers, for example, and without a salary cap committed teams could outspend for top talent. I believe Shula was still a great coach, but maybe had become a bit complacent with his coaching staff. I still don't understand why he stuck with Tom Olividatti so long. There were a lot of bad drafts too so blame has to be passed to the scouting department and Shula who had the ultimate say on who the team picked.
I think part of the problem was that Marino was so good that he masked how bad the team was (after 1985). The best Dolphin defensive players retired and the unit just absolutely collasped. But, the Dolphins still won enough games to stay around .500 or in the playoff hunt (good coaching, Marino). Because of that, they never got a chance at the top players.
The fact that Shula couldn't get a running game going to compliment Marino is a bit of a head scratcher, since he had the most effective running game in the early to mid 70's.