Forgive me if some of this is already in, but the Wiki makes no mention of it, so...
* Higher-quality millstones and querns should grind faster when made into the appropriate building.
* Higher-quality mechanisms should likewise make those workshops that require mechanisms operate faster.
* Higher-quality mechanisms in a pump should make the pump less tiring for dwarves who manually operate it, and maybe reduce its power requirements when automatically powered.
* Levers made from high-quality mechanisms should take a bit less time to pull (or, conversely, low-quality levers should take a bit more time to pull.) The extra time for a low-quality lever should be sort of random so players can't account for it, ensuring that high-quality ones are better.
* Likewise, linkages made with high-quality mechanisms should transmit their effect very quickly, while linkages made from low-quality mechanisms should take longer in an unpredictable fashion.
* An anvil's quality (and material) should influence the time it takes to make something with it.
* Higher-quality bags should speed up any job that uses a bag (gather sand, processing to bag, etc.) Also, perhaps the bag should be a bit lighter -- which is an abstract representation of the fact that they're better made to carry stuff. (Less wasted material, or something.)
* Higher-quality ropes and chains should take more time to link/unlink creatures to. Ditto for cages and caging.
* Pick quality and material should influence mining speed.
* Any workshop designed by an architect should have a increase to its job speed if well-designed; and if it involves items with quality in its construction, high-quality ones should help, too. Also, well-designed workshops should 'resist' clutter, and require more items before they count as cluttered.
* Any potentially mechanical device (bridge, etc) that can be designed by an architect should have a faster and less random reaction speed if well-designed; and if it involves items with quality, again, those should speed it up.
* A well made from higher-quality components should be faster to drink from.
...I do not think that most of these things should have a very big influence, since it would be a bother if players absolutely had to replace all their workshops, and since a bunch of masterwork stuff could add up fast. But it should show at least some impact, even if it's very minor, so players have reason to want higher-quality stuff in all cases.