Several Very VERY critical points for a successful mecanum drive:
-SQUARE FRAME. Not as in length (though a square shape IS the most efficient for mecanum), but as in straightness and lack of vertical warping. That is, all 4 wheels need to be perfectly level to get ideal force distribution. If you are worried about having a lifted wheel, put some sort of rubber or spring mount to allow the robot to settle in a planar configuration. When you design the robot, try to create close to a square shape too. We did rectangles both years, but the only way that works is with a "narrow 'bot" configuration. ("wide 'bots" will not work well!)
-WEIGHT DISTRIBUTION. When you construct your 'bot, try to keep your CoG in the center. Not forward, not backward, not left/right, but dead center (ideally). Having a shifted CoG will cause one wheel to have more traction than others (f=uN) and will cause the robot to skew, particularly when strafing. In all drivetrains, low CoG is ideal, so that too, but less importantly.
-DRIVER EXPERIENCE. your drivers need TONS of practice, even if that means playing around with just a base for a while. Know the ins-and-outs of mecanum, and it is advantages. As previously mentioned, mecanum has poor pushing power, but with a skillful driver and well made mecanum (coding is a major factor), you can use the agility to dodge even the toughest defensive 'bot. In 2011, we burned a jag mid competition, and had to compete a match with just 3 operating wheels. From a spectator's perspective, you would not have even known the difference. Of course, holding "up" on the joystick did some funky things, but it was easily correctable for a guy who knew what was going on.
-CODING. Make sure you use encoders, as wheel speed is the single most critical factor. I'm not a coding expert (hardly a grasshopper), but perfectly calculating wheel speeds in all situations (try driving forward, while strafing left, while turning clockwise. Imagine what the wheels have to do!) will really give you an advantage. This is probably the most daunting problem teams have when building mecanums, and where most teams who have tried it and hated it went wrong.
If you don't already, depending on your driver's preference (Xbox or Playstation) get either a wired Xbox controller, or a
Logitech controller. (wireless Xbox 360 and PS3 controllers are illegal, and I dont think there is a wired PS3 controller, hence the basically identical Logitech). Driving a mecanum robot is a lot like playing a first-person-shooter. Configure the joysticks to replicate how you would play Halo or Call of Duty, except without the "look up/look down" axis. This will make driving feel far more natural to drivers, and will let almost anyone have the basic ability to drive the robot instantly
Both years we did mecanum (2011, 2012) we used toughbox nanos (I dont know the ratio) with mecanum wheels directly on the output shafts. We built custom assemblies to house each wheel including our
deflector plates for hopping the bump in 2012.