To sign free agents outright over the approximately $5.5M MLE level (you are allowed to sign up to $5.5M a year on free agents if you are over the cap) you have to clear cap space below the salary cap level $58 million. Basically the Heat got rid of everybody, cleared $30M + in cap space, allowing them to sign James and Bosh to max contracts (they took like 10% discounts to get Miller as well). They then got over by $58M, was signing Anthony who they were to able to get a cheap cap hold on, and signing veterans to league minimum contracts about a $1M each. You can sign players to vet minimums if you are over the cap.
The luxury tax threshold is about $72M. That has no impact on who you can sign with the MLE (but can't go abovethat because you over the salary cap), but every dollar above the tax thresholdyou have to repay to the pool, which gets distributed evenly amongst teams below the tax.
BC had no ability to sign anybody this offseason other then MLE, because he blew it on Hedo Turkoglu last offseason, who he turned into a somewhat overpaid Barbosa. Add in the fact that he overpaid Bargnani, Calderon, and wasted the MLE on Kapono which he had turn into another bad contract in Evans (as solid as he was). He was also stuck with Marcus Banks who he "had" to take on from Miami in the brutal series on O'Neal deals which he lost two first rounders in. (Basically getting rid of Banks was key for Miami being able to clear cap space for signing Bosh and James).
Basically just an awful GM job -- but he has done fairly well since Bosh left,