I'm extremely thorough whenever I do playthroughs of the game, because I test it the same way that I'd expect the ideal beta tester to.
The reason we've been in the alpha stage for so long is because there have still been bugs present in the source that we've known about, and the idea of releasing a beta (to me at least) is so I personally can't find anymore bugs in the game. Why allow the beta testers to report things we already know about? That would be wasting both their time and ours. As far as I know, I'm releasing a bug-free version game for the beta testers to try and break. If they find something, it's interesting to see exactly what that is, because it means it must have slipped past my own rigorous testing phases.
In short, yeah, this means the game's pretty stable right now, but there are still some obscure bugs that we're aware of and have never been able to track down. Hopefully feedback from the beta testers will help to root these out and zap them for good.
Other tasks beta testers will be required to focus on are thoroughly testing the points scoring system with all classes, in all different ways. Testing the combat system, and testing the... well, I can't reveal that one just yet.

Suffice it to say, that to be a potential beta tester, you should be thinking in terms of repeating actions a great many times over and watching for little numbers to change on the scorebar; restoring and then trying all again another way. Or trying to break the combat system, then noting down a bunch of variables to report back to us, along with an exact description of what they were doing at the time.
Testing this game will require a lot of commitment, so here's hoping we get saddled with reliable testers! You'll all get to play the game sooner if we do.