I created a wiki page detailing Snow Leopard compatibility issues.
Presently two exist which have workarounds described on that page. I will release a new build shortly (that means, I planned to have it out by now ;) ) which incorporate these workarounds.
There are (or may be) issues with some of the bundle commands written in ruby (as Snow Leopard ships with ruby 1.8.7, which isn’t 100% backwards compatible). We will address these as we see them over the next weeks/months and updated versions should appear in the Subversion repository.
Before you Upgrade
If you do a clean install of Snow Leopard, make sure you have your TextMate license key handy! It can be requested from this page. If you have changed your email address since you bought the program then you can copy/paste the license key from the application by using the “Change License…” button in the dialog which appears when you select the TextMate → Registration… menu item.