Just a short condensation from what ive read so far and my personal ideas:
1. Workshops should have a setting for speed/quality of work
2. Raw material should have "units" in it, with different items consuming different amounts of "units"
2a. The amount of units in a rock/tree/whatever could be influenced by the miner/woodcutter/etc
2b. Workshops should show how many units are left in it, and dwarves should attempt to finish using all the units before getting new material
2c. Any spare units left that cant be used for finishing an object can be stored in a bin/stockpile, and then later grabbed to finish something else
2d. Horribly mismade items can be broken down into a few spare units, then being stored/used again
3. The original starting seven, in addition to the skills you allocate them, should be able to do any job at slightly below dabbling, thanks to the pre-expedition guides/tests/lessons. If a dwarf showed proficiency in those tests, it could give them a free dabbling skill, as well as being mentioned in their profile. "This dwarf shows aptitude for < PROFESSION>."
4. Refuse might be generated from the epic failures, such as the shattering of a gem, but it might still be usable. For example, if a gem shatters, it could still be used as decoration. "This item glitters with shards of < GEM>."
5. Rough buildings shouldn't have a failure chance. If you're just stacking some blocks and cementing them together, or just laying down some planks for a rough floor, then you shouldn't fail. This might come into play once enemies can smash through (currently invincible) constructed walls.
6. The POW idea is intriguing. If some sort of interaction system is implemented, then i see some intresting options becoming available.
6a. If you have POW's, say, goblins, then you can force them to use the horrible failures of your trainee stonecrafters, such as mugs and bowls.
6b. On the other hand, if they behaved, then you might assign them better quality items. This option would be in the main menu, possibly under "Orders -> Prisoner Treatment".
6c. A masons or carpenters workshop could be built in your prison, then you could order goblins to carve out stone or wood blocks, which would take no skill, since they're just sawing/cutting stuff into cubes. (I know this isnt true in real life, its not that easy to get a good block with little effort, but this is DF, and the "no fail" setting applied to building rough buildings and making blocks should help a bit in training dwarves).
6d. If you treat your prisoners well enough, they may be motivated to work better/faster, and may even become better stonecrafters/woodworkers, eventually churning out better quality items. By extension, if they learn the trade well enough, and you treat them good enough, they might defect and join you, adding to your skilled workforce.
7. All crafting trades should have a couple "no fail" crafts, in order to help train. Examples: beds(just making rough planks attached to a couple supports, prisoner quality, can be improved with cloth/leather covers), blocks of any type(as you're just cutting stuff into cubes, see 6c), making coal into coke(yes, i realize that this actually involves careful monitoring of temperatures, but again, see 6c.), etc.
I realize that some of these suggestions are impractical and unrealistic, but hey, if a video game was completely realistic, why would we need real life? Anyways, thank you for reading and considering my suggestions, and thank you for posting the ideas that i shamelessly ripped off.