I'm better at UT than I ever was at 200X, with all of the double-jumping and what not, so my tips will probably be most effective in UT.
I'm a terrible shot, so I don't mind just giving splash damage with rockets or the shock combo.
What he said. Even if you have terrible precision you can still do very well with the splash damage from the flak or RL. I wasn't so good with the shombo or the rifle but I could place a flak shell almost anywhere.
When using the flak, jump and launch your shell at the apex of the jump to give it some extra distance for those long range shots.
A lot of people think the goo gun is useless; I disagree. Try loading it fully with Altfire and then dumping your load (har har) on a wall right in someone's path. If you time it right it's almost always an instakill. If not, it still does massive splash damage.
The translocater can be a very effective weapon (telefrag) in gametypes that use it.
In UT, the dodge jump can be used to 'lateral' yourself between two platforms very effectively. It'll take you a good bit farther than a regular jump.
Aside from those basic techniques there's really nothing special to it. Just keep moving and dodge a lot. Timing pickups like the shield belt can really allow you to dominate other players, because you decrease your chances of dying while also increasing theirs by depriving them of the pickup.