A GH-2 might suit you well, but for sports, its AF may not track fast enough.
Right now, for sports, a Sony A77 that will autofocus while shooting video might be the best choice.
The new Nikon mirrorless cameras are supposed to beat all others when it comes to autofocus, but you lose shallow depth of field due to sensor size, which is the main advantage of video with DSLR.
If you are watching videos on a computer monitor, there are lots of issues that could make them look bad or excellent, a lot of it has to do with skill and post processing tools. Moire can be reduced in post processing, but it is better to remove it at the sensor, which is what we will likely see with new sensors coming out for future models.
Still, thousands of professionals seem to deal with it, even for major motion pictures and television shows.
Unfortunately, DSLR's are not yet developed to operate like consumer or professional camcorders with ready to view output, it takes practice, knowledge, more practice, and a developed skill to get the best results. Thats just one of those disadvantages of early stages of a new technology, still a bit rough around the edges, but good enough to be desirable for those on a budget, and we all are. If you can produce a advertisement, for example, at a cost below the competition and still meet or beat quality standards, you have a advantage.
I would suggest you assess your willingness to put up with a difficult to use technology, having to spend several times the cost of the body in accessories for truly professional results versus just hanging on to your camcorder for one or two more years until they can meet your needs.
In any event, you are looking at alternatives and thats the way to do it. In a fast changing field like video by DSLR, obsolence happens quickly.