I am interested in learning level design. I have the Unreal Editor that came with UT2004. Is that good to begin learning on?

I wouldn't worry about software too much. I think the important learning process with level design is experimentation and developing a good understanding of overall game design.

It would be good to pick up some books on the subject of game design, art and level design. I expect the UT editor is a reasonable place to start, it's a good game and will let you see how your ideas work without too much fussing.

If you're looking at learning how to use an editor such as Unreal Ed then you will be learning the necessary skills for world building. However, world building and level design are not the same thing.

Level design is concerned with premise, concept, gameplay elements/events, composition, functions, and pacing. World building is the process of taking your design and creating the final environment and assets to bring it together in a functioning game. If you're already confident with your level design abilities and are at the point where you want to start implementing them in a functioning level then learning an editor such as Unreal would be an excellent place to start. Half Life Source, Crytek's engine, and id's Doom 3 engine would also be decent alternatives to consider.

I work for Liquid Development, which creates the art assets for dozens of high profile game developers. So far I've worked or have been working on the art for 7 next-gen games for the PC, XBox 360, and PS3. At least a third of the developers that I've worked with are using the new Unreal 3 Engine so learning Unreal Ed would be tremendously helpful for acquiring a job almost anywhere in the industry.

If you learn the editor that comes with UT2004 you shouldn't have much difficulty learning the new Unreal 3 Editor when it's released because much of the interface and functions have remained the same. The most significant advancement is in the physics and the material creation/application within Unreal Ed. Creating materials in Unreal is very similar now to creating shaders and materials in Maya's hypergraph. So if you're familiar with the hypergraph in Maya that will also be a big advantage. If you're not familiar with the Hypergraph don't fret, learning materials in Unreal isn't too difficult (at least not the basics).