Is Digging only for quests?
Actually, digging isn't just for breaking piles of flat rocks up for quest items, you can also use it around diggable areas and if you get lucky, you might get a good item!

How lucky is lucky?
Go ask the other players, they'll tell you to blame US LaTale's abyssal item drop rate or something.

Is it worth using my time for?
Digging in Latale Ely is like gold mining, you'll use up a lot of time in the task, but if the RNG doesn't hate you and drops something cool (no, not Level 141+ Cherryade), then you can celebrate! Oh, then you can sell it or brag about how you beat the game in a staring contest.

How does Digging work?
Excavation spots doesn't vary by random luck (though their item drop rate does), it's actually an invisible non-mobile mob that spawns anywhere on a walkable surface (there are specific areas that can contain these mobs).
You just use Dig to "attack" the ground. If you miss, then nothing happens (and digging in the same spot doesn't work unless someone defeats a mob elsewhere on the map and it happens to spawn on your digging spot), but if you hit the mob, then you have a chance to get an item.
Whether you get an item or not doesn't matter when you dig up a hole, however, after you "attack" the mob, it's defeated then it respawns in a different place within the same map.
Even with all this data, it is still a data that can't be tested due to the game's item drop rate. However, with comparsions to the information that the Behemoth's mouth in Field Area and Field Fork does the same except with staying at the bottom level of the map, this is a probable theory at that.

Does it matter where I dig?
Yes, it does. It determines which fashion items you can get since each location has a different set of drops.

Is there a list of where each is?
Of course! Just look here: JP Latale Ely  Digging List
(Yeah yeah, I know, but I accidently destroyed part of a translated list and I'm running short on time right now.)

Is there a good market for this stuff?
As of 10/14, not really, since there aren't many out there in the first place. You could earn a pretty penny right now, but it might be better if you wait it out.