At this point, aren't the Patriots the most hated team in the entire NFL?
It is interesting how that list changes over the years, though. In the 1970's, Miami's nemesis was the Oakland Raiders and that was the team I hated the most. The Raiders were the team that stopped the Dolphins from getting to four straight super bowls, and stopped Miami's win streak at 18. At one point, Miami was 3-13 against them. It's closer to even now.
The Jets were probably the team I hated most in the 1980's. For some reason, when Buffalo was really good I respected the heck out of that team. Hated the 49ers when they were good.
With Miami being so mediocre year-after-year, it's harder to hate teams. It's not like there's one or two teams holding the Dolphins back. It's more like their own front office.