So here's what I did. I sorted all ~200 or so of our 5-man units by descending Offensive rating (points per 100 possessions), and then used my rudimentary paint skills to delete all the lineups that have played too few minutes to find any statistical significance. The results below. Ps, the column headings for the big block of numbers are: minutes played, Heat possessions, opponent possessions, heat points, opponent points, Heat offensive rating, opponent Offensive rating, and then differential between Ortg and Drtg. So the offensive rating column is 3rd from the right. Sorry I forgot to add that when I made the graph in paint

Sorry about the size...unavoidable. You have to open in a new tab and give it a couple zooms to get a readable chart
Consider that league average Ortg is 104.4. Also, on the season Miami's Ortg is 108.2, and 109.9 is tops in the league. So, the Heat have 11 lineups with an Ortg over 108, up to 125, and then there's a big drop from 108.81 to 104.84 (11th best Ortg to 12th). Then look at those below average to just plain awful lineups (Ortg below 105), and the one thing that stands out is the frontcourt:
Haslem/Bosh
Haslem/Pittman
Haslem/Bosh
Haslem/Bosh
Haslem/Bosh
Haslem/Bosh
Haslem/Bosh
Bosh/Anthony
The 2/3 combos in those lineups aren't nearly as consistent, and feature a lot of Wade or Lebron + shooter:
Battier/Lebron
Battier/Lebron
Battier/Miller
Wade/Lebron
Battier/Lebron
Wade/Lebron
Wade/Battier
Wade/Lebron
Although Battier's name jumps out there too, he's also in a bunch of lineups with Ortgs of 108 or better, 5 where he's paired with Lebron at the 2/3 and 2 with Wade at the 2/3 (and one with Miller and Lebron at PF).
Haslem/Bosh, on the other hand, are only in 2 lineups that are top-shelf offensively:
Cole-Wade-Miller-Haslem-Bosh
Wade-Battier-Lebron-Haslem-Bosh
Joel only makes 1 appearance in the bad lineups, though its really awful lol, Starters with Cole in place of Mario is just atrocious. But Joel is in 7 of those 11 great offensive lineups. Very surprising.