In 5 simple tasks
1. LeBron work on your post up game.
For some reason during a playoff series he'll either need to rely on his jumper or his post game. For the first 3 series he was able to consistently knock down the jump shot. Something he failed at during the finals vs. a very good defensive team. You're right you do have a lot of work to do this summer, well if you want to get any where next season.
2. Erik Spoelstra's ability to open up the offense
The Heat have one of the most defensive minded head coaches in the NBA, but without a coach who has a clue on the other side of the ball you're not going to win championships. I think the old saying defense wins championships is only half correct. It's offense that also wins. How many NBA Champions do you see who win games 88-83? Not many. Look at the Mavs. Avery Johnson preached defense for year with the Mavericks. And like the Heat they fell short of a title in 2006, and years later with a very good team. Rick Carlisle comes and shows the Mavs how to play offense and break up a defense and boom, championship. They took what they learned from both coaches to win a title. The defense from Johnson and Carlisle's offense. Carlisle's zone defense in the Finals did work wonders too. It's either Coach Spo learns offense or time for a new coach. Look what basically a street ball offense got the Heat in 2011? Two games from hoisting the Larry O'Brien trophy.
3. Improve chemistry
The big 3 are still in the "process" of learning how to play with each other. While the media and Coach Spo keeps feeding us that we come to realize this teams been with each other for over 100 games already. I expect by next season for the Heat to fully mesh, but even then they'll be some next pieces around the team. Which will be points 4 and 5.
4. Get Center
With the limited cap space Miami has they'll have to pick up a center. Rumors point toward Samuel Dalembert. Which I wouldn't mind because he help with the rebounding game. But I'd also like to see Joel Pryzbilla, Spencer Hawes, or Deandre Jordan in a Heat uniform. Tyson Chandler and Greg Oden would be dreaming and Marc Gasol or Nene is never going to happen.
5. Get a Point Guard
You need to have a true point guard. I'm tired of Bibby/Chalmers/LeBron/Wade all bringing up the ball. It's too much, the offense needs to be used to one guy distributing the ball from the top of the key. Well not one guy, but we need a true point guard. Bibby is losing his gam and Chalmers is not careful with the rock. LeBron and Wade could be careless sometimes, but overall they're solid passers. Especially LeBron. Maybe an Aaron Brooks, Goran Dragic, or Stuckey. Steve Nash isn't a free agent, but maybe the Suns will eat that contract so Nash can win his first title. This is a perfect situation for him.