The Heat own Wade's bird rights, which allows them to pay him up to the maximum (around 20 mil) and go over the cap in the process. The only thing his salary impacts this season is Arison's wallet, since it will push the Heat into luxury tax territory and since they've been there a lot lately the penalties are steep. I don't think Riley is terribly concerned about that, but handing him a multi-year deal eliminates most free agent options for 2016 and means that this is the roster the Heat will be riding with for the next 2/3 seasons.
After signing Wade Riley may trade Chalmers and/or Anderson to lessen the tax hit, but I don't think there's much of a market for either of them and Riley doesn't have any picks to package with them to entice some team that's under the cap to take their salary on.
To me this is a flawed roster and I have a tough time seeing it work without a guard that can break down the defense. Whiteside is an awesome presence but his lack of skill limits what you can do, much like with Jordan in LA. Its worked in LA since they've got the best offensive orchestrator in the game, but they still get exposed by the better defensive teams.