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.
Before the advent of cheap high-speed Internet, it was a common test of lateral thinking among network engineers to ask students or newbies what the fastest method for sending [x amount of data] was. While the disciples argued at length about protocols and pipes, their more experienced colleagues would point to the Post Office. In the story, cue Ridcully deciding not to send a simple, short message that the clacks would send in a matter of hours, but an entire book with color illustrations (which would translate into an enormous amount of code). So even though it was ultimately unnecessary (and Moist had raised the stakes by reducing the Trunk's delivery to just thirty pages), there was a possibility, however remote, of the mail coach to actually outpace the transmission of the entire book. After all, not only would a whole book require coding into semaphore signals (color illustrations included), it would also fill up the up and down lines, require a LOT more error handling and correction, and would actually slow down at the terminal tower —where it would be forced to wait for the signal queue to be cleared as it was transcribed back into a book. With color illustrations. And then the transcription would still have to be delivered to the intended recipient.