I've had the same problem with the Dissolve Tool since moving to 10.1. I first noticed it 2 weeks ago in a model built in 10.0. After a bit of time spent looking for solutions I rebuilt the model in 10.1 and it seemed to solve it.
However the problem had recurred again today in another basic model and the rebuild option has not worked this time. After testing the tool inside and outside of models I have seen the multipart problem also occur when running outside of a model - but not every time, and am unable to reproduce the error consistently.
When trying to repeat the steps of the model with just the standalone GP tools the multipart feature worked one time, but then a while (after a few other select and dissolve tools) later failed to work on the same input with the same Environments?? (Image of GP results attached)
The only thing so far that I can see that may be consistent is the select tool? The multipart dissolve has worked when I put a definition query on the layer and then Dissolve, but fails to work if I use the Select tool to create an intermediate selection matching the definition query, and then dissolve. And then fails to work subsequently after the select has run? Not 100% sure on this but I will do some more testing over the weekend and see what more comes of it.
Hopefully we can resolve this issue soon as the dissolve tool is my most commonly used GP tool.