In the Buckbeak execution scene, I'm almost certain that Dumbledore is in on the mission for the hippogriff's "break-out"; The scene makes it very clear that Dumbledore is purposely stalling the Minister from looking towards Buckbeak, which would reveal the escape - He does it over and over, just barely giving Harry and Hermione enough time to escape with the hippogriff unseen by the Minister.
Later that night, Dumbledore, upon hearing of Sirius's innocence, suggests that Harry and Hermione go back in time to save "two innocent lives", one being Buckbeak, and the other Sirius.
How was it possible for Dumbledore to have been in on the plan that he didn't set in motion (or know to set in motion) until many hours later?