They released Mike Miller via the amnesty provision, a move that ultimately saved the Heat $15 million in luxury tax. James complained about this frequently during the season, especially on nights when Wade missed games to deal with ongoing knee issues.
In conjunction, the Heat did not use their mid-level exception to add a role player to help replace Miller. After signing Ray Allen and Shane Battier with the mid-level over the previous two years, the Heat added reclamation projects Michael Beasley and Greg Oden instead of a proven backup.
Third, at midseason the Heat traded Joel Anthony, a future first-round pick and $1 million in a cash-dump deal in which they ended up with Toney Douglas. The Heat could've used those assets in a different type of deal, one that provided immediate help and wasn't aimed at saving tax dollars.