[jvriezen]

We've also used open loop mecanum in 2011 and 2012, and had no issues worth addressing regarding wonky control.

Four wheels touching the floor with comparable force and correctly spinning rollers are important of course. We took care in design and construction to make that a non-issue. A suspension can help here. (We designed one with suspension, but due to issues removed the suspension)--- our well engineered wooden bot frame may have provided enough 'give' to allow more even weight distribution than a more rigid metal frame would have provided.

If things are noticeably misbehaving, I have my doubts that changing from open loop to PID will resolve everything.

Get four bathroom scales on a level floor so that the scale platforms are level with each other and see how much weight is on each wheel. Of course, if the scales are different models, their heights will be different, so you might have to shim some under the scale feet. If the scales aren't calibrated the same, you should be able to compensate by weighing 4 times, rotating the bot 90 degrees between weighings, Add up the 4 weighings for each wheel. We never actually did this with our bots, but that's because we didn't have issues with driving them as built.