“He’s useful,” Sirius muttered. “Knows all the crooks — well, he would, seeing as he’s one himself. But he’s also very loyal to Dumbledore, who helped him out of a tight spot once.
What did Dumbledore do for Mundungus that would cause him to be so loyal, to the point that the Order wants him to help with such an important task as moving Harry in the last book? Sure, Moody didn't trust him completely, but they still thought he was one of the useable people, and while Dumbledore was around he seemed to trust Mundungus as much as he trusted others.
Why was Mundungus unquestionably (or was he?) loyal to Dumbledore?