Replace caucuses with open primaries -with the sole exception of Iowa. Also, adopt the rotating regional primary system.
Otherwise, I don't really see much else that needs to be improved. I like our proportional pledged delegate system (as opposed to the GOP's winner-take-all approach), and the super-delegates serve to prevent unelectables from winning the nomination (and it usually works). Though I am open to reducing their numbers somewhat.
An unmentioned problem with a rotating primary or other date changes is who would pay for it. Many states like IL use the date of the legislative/congressional primary as the date for the presidential primary. States don't like to shift their main primary date as it affects the whole state election calendar from filing petitions to post election certification. Moving the presidential primary would force the state to have two primaries at twice the cost to the counties that conduct the election. What is the source of those extra funds for the counties?