While I don't have experience with the Mecanum drive, our team has done a harmonic drive for a couple of years which is pretty much the same thing. When we first put together our drive the chassis would steer off in random directions because the floor (and no floor will be ,ever) wasn't perfectly flat (we had shimmed the wheels to be flat). This is why you use a suspension so that all wheel can stay in contact with the floor and cause good control of the vectors. Our first suspension was with each wheel mounted on a hinge and a spring, this would tilt whenever the robot would accelerate in any direction. So this year we used a "tractor" type of suspension. This didn't add any weight really but kept all wheels in contact always.
http://www.chiefdelphi.com/media/photos/22700
We also added a rotational accelerometer to keep track of any variation in the bots direction of travel and last year when I broke out our original chassis for the first time in months so the programmers could work with it one of the motors wasn't plugged and we didn't notice. Despite the lack of an entire vector the accelerometer allowed the robot to drive straight (if a little drunkenly).
Hope this helps
Alex