At several times during the book, Moist is referred to as delivering to the gods, or as the "Messenger of the Gods." And the statue formerly gracing the post office is clearly a reference to Hermes, with the winged sandals and all. Now, while Hermes was certainly known for his speed, the messenger of the Greek gods was also very much a trickster god—"excellent in all the tricks," in some translations. Appointing a con man to be Postmaster makes even more sense now.
Vetinari has more than one reason to feel smug when Moist forfeits his stolen money to keep the Post Office going. Not only is he vindicated because Moist shows he's become genuinely committed to his task, like it or not, but he's also pleased that the amount of money Moist retrieved is exactly the amount the con-man had stolen in the first place. As in, Moist never squandered any of it on luxuries or vices, meaning he's likely to avoid the perennial bane of Patricians — getting fat, spoiled, and venally-corrupt — if (as many readers presume) Vetinari intends for Moist to be his successor.
Moist is a very unfortunate name, as everyone points out in different ways. But when people get moisture on them, they can be kind of slippery...like a con man. Adora Belle's calling of Moist "Slick" works on that level, too.