We have just left Bolivia - we travelled across part of the Salar de Uyuni in early January.
We only drove from Garcia to Llica, about 30km across the salt, and at that stage it was covered in about 2-5cm of water.
We weigh 5000kg, but we had no problems on the salt (we would never have risked it, except that we saw a 60 seater bus crossing the other way).
On the other hand, just a few kms back we went out onto the mud flat and got horribly stuck. I estimate we´d have been working for 2 days to extricate ourselves - assuming no rain - if we´d not been offered the services of a tractor. We´d already done a couple of hours´ work, and made about 4m of progress.
So, while the salt was very firm even when wrt, the same cannot be said of the mud, usually around the periphery and in the smaller pans in the region.
On our way back across the Salar, a few days later, there was less water on the salt, but some places still had several cm. Lots of 2WD taxis and buses were crossing - some from Llica to Uyuni which is a long way.
The pans were amazing - worth every horrible km of road to get there. The further you are from the Salar, the worse the reports you hear. Once you get there, you can see for yourself if other vehicles are crossing!
For a bit more detail, and our evening GPS waypoints, see our website.
Hope this helps.
Michael & Sandy