As WHBM says, the H-1 replica crashed in the summer of 2003 on its way back from Oshkosh, killing owner/builder Jim Wright. Don't know whether they intended to use it for the film or not, but I would have assumed so.
I have to say that I don't see Leonardo de Caprio as ideal Howard Hughes material, but then again Tom Hanks, excellent actor though he is, never seemed like the best choice for Jim Lovell to me either - but Apollo 13 was a great film!
I look foward to seeing the Aviator when it comes out on DVD, unless I unexpectedly go transatlantic while the airlines are showing it...