To vote for either Dean or Lieberman you have to register as a Democrat.

Trying to mess up the other party doesn't make sense if you want a say in who your party's candidate is. If your preferred party is all sown up, it might have some benefit. Given that Bush is likely to have little opposition, I'd expect more Republicans to switch & try to mess up Democratic primaries than the reverse. If the Democrats end up with someone unelectable, maybe it can be blamed on the GOP?