[Rob Stehlik]

This is actually a very good question, one that I would like to see some answers for as well. Dealing with backlash on a heavy arm is inherently a mechanical problem, so tuning your position control code won't get you very far. Obviously higher precision gear meshing and shaft coupling would help, but within the fabrication capabilities of most teams, this isn't a realistic solution.
I tend to agree with Andrew that adding friction to the system is a good approach. Generally speaking, once you gear an arm joint down to a reasonable speed you usually have torque to spare, so a little extra drag won't be a problem. If you can add enough drag to prevent the arm from wobbling on it's own without straining your motor too much, you're in business. In 2012 we had a lot of issues with overshoot and oscillation on our shooter turret. I ended up making a brake band out of plastic to add some drag to the turntable bearing, and this helped a lot. It's best to have some method of adjusting the amount of drag, so you can set it to the right amount, and compensate for wear over time. A simple way to check that you aren't adding too much drag is to measure the motor current while it is running.