Everyone loves Dunsparce, but no one loves to be on the receiving end of its haxing skills. I believe he is always a good choice for a UU team. He can take a fair few hits, and deal back some slow, steady damage, while the opponent can't do a thing and you restore health with Leftovers! Just don't overestimate his lifespan and be too risky... but other than that, have fun!
Dunsparce is a highly diverse Pokémon; I find it works better as a physical sweeper in an UU game. Flinching enemies constantly with Serene Grace + Headbutt is very annoying, and no Pokémon will score it more than Dunsparce, especially when a paralyzed foe is left in. Basically, use Thunder Wave (or Body Slam if you want the 60% chance of paralyzing a Ground Pokémon), maybe again if you predict a switch. Then Headbutt or Rock Slide for some major flinching!
Shadow Ball is really only there to hit Ghosts, and with repeated Special Defense drops, it can trigger a switch later on. Rock Slide is primarily there to take out the common Jumpluff, Fearow and Swellow, but if you decide to risk using Dunsparce outside of UU, you may be able to score a kill against Skarmory... something I have managed to do with this Dunsparce many times.
Quite a few options here, most of which take advantage of Serene Grace. That 20% chance of a full stat boost from AP is always good, which can potentially make Dunsparce a good Pokémon (:o indeed!) Glare can paralyze more Pokémon than Thunder Wave or Body Slam can, being able to hit both Ground and Ghost types, but that accuracy winds me up sometimes. Ice Beam has that 20% chance of a freeze, but I don't use it much, as Dunsparce is all about paraflinch. Water Pulse has a 40% chance of confusion, quite chancey, always up for consideration. Attract can get piss annoying, and will at least force a switch, as does Yawn, but remember it doesn't go hand in hand with paralysis. And Counter is a nice surprise; you don't see it much on this Pokémon.
I usually max out HP, load quite a bit into Attack, and distribute the rest into its defenses. Go with Adamant. Unless, of course, you do decide to use one of those special attacks.
Checks and Counters
He may have a buttload of HP, but he can't really take a strong attack, least of all a Brick Break. His slow speed leaves him susceptible to status effects as well, like sleep and so forth, shutting down his whole operation. Watch out primarily for the likes of Machamp, Hariyama, Jumpluff and friends. And getting burned by Banette is never cool.