My assumption as far as the "Dumbledore should know Sirius is innocent" thing has always been that Dumbledore knows Sirius is innocent, but believes he blew up a street full of muggles to get revenge on Peter. He knows if he comes forward about that, Sirius will be let off, because Peter would be considered more evil and muggles of no consequence. Dumbledore disagrees, and let's sirius rot in prison for those 12 murders, as opposed to the Potters. (C) Ramenth on Spacebattles