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 that would be even larger if the code also specifies typefaces, page layouts, and formatting). 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. In fact, very large amounts of data are STILL quite often delivered by couriers or Fedex (and in at least one instance, carrier pigeon) on high-capacity drive rather than going through the massive trouble that downloading can represent.
Moist's good working relationship with the goddess Anoia might have a deeper reason. The golems, who are very good judges of character, say Adora Belle reminds them of Lela the volcano goddess. A later book reveals that Anoia is Lela. Basically, she's his type, and he hers.
A funny thing said by Anghamarrad about Lela was the fact she was fuming because the Rain god always rained on her lava. Adora Belle smokes, and Moist enjoys riling her a bit. Looks like they found each other.
Vetinari's speech about believing in angels makes a lot more sense when you realize that the word "angel" is derived from the word for "messenger".
Why does the mail choose Moist as their avatar, when they had several other candidates to choose from? When Moist is lost in the post office and discovers how the other postmasters died, he decides to say his Famous Last Words again: "I commend my soul to any god that can find it." The mail, sort of a godlike entity at this point, was listening.
Why is Moist so much more of a despicable person in the movie than the book? The book is written from his perspective. He's a slightly Unreliable Narrator, and would interpret things positively for himself. The movie is an objective third person.
It's a proven fact that dogs react to body language and vocal tones. Moist was confident in his ability to command the canines the other mailmen set on him, manifested no fear and was authoritative, which prompted the dogs to obey the "dominant male" in spite of their breed being misidentified.
Since this book establishes that particularly-talented condemned prisoners occasionally get "executed" and transferred to positions that suit their talents, this retrospectively raises the possibility that Carcer is currently running a civil service job somewhere in Ankh-Morpork.
Just this tropers opinion - No. Vetinari would not disrespect those who died like that. And Carcer doesn't believe in angels.
Plus from a practical point of view Carcer is uncontrollable. Vetinari can take steps to contain Moist and ensure that he does a good job, Carcer is much more of a wild card, you let him loose and he's liable to start murdering people for fun. Not to mention that employing him would be almost guaranteed to turn Sam against Vetinari if he ever found out.
'Almost' nothing. If Vimes found out that Vetinari let a cop-killing psychopath (who directly threatened Vimes' family) back out into the world, he'd depose Vetinari himself.