Unfortunately, it looks like I'm actually the only person from that group who's still noticeably active. I might be able to get it going again, but I dunno.
Anyway. Beta-reading really only requires that you have eyes (or an extremely good screen-reader, I guess), that you're good at recognizing what's actually on the page rather than what your brain thinks ought to be there, and that you're not afraid to offer clear (but polite) critiques. (My fatal flaw as a beta... okay, the first one is procrastination, but my other fatal flaw is a tendency to ask rhetorical questions when I should just say "this part was confusing because XYZ; here's how it could be improved.") Explaining the problem clearly is very important, as is being able to suggest a solution whenever possible. Sometimes you won't be able to put your finger on it, though, and saying "I don't know, it just feels off" is okay. Being able to notice and compliment things that were done well is also useful, and unfortunately, few of us have that skill. We should all strive to improve our skill at giving positive feedback.
One important rule that I learned from my editorial internship is that you never give a "correction" based on your personal style preferences; you should always have a sound, objective reason for making a correction. I refer to the Chicago Manual of Style as my ultimate authority, since that's what I was taught, but most style guides agree on most things that come up in fiction; they only differ greatly when it comes to citations, which aren't an issue here. You'll definitely run across differences in British vs. American vs. Canadian vs. Australian usage (and more, no doubt), so learning to spot those is important. You'll pick it up as you go, but when in doubt, always consult a reliable source. (I've occasionally found good style guides for different parts of the world on university websites.) Also, always doubt. If you can't suspect yourself of being ignorant or mistaken, you can't learn, and you can't help anyone else learn.
As a writer, when I'm looking for feedback, I always want to know how my writing is affecting the reader--did the funny parts make you laugh? did the sad parts make you cry? when the agents got hurt, did you worry about them? etc.
As a beta, though, I typically can't focus on that sort of thing until the SPaG and other distracting mechanical issues get cleaned up. That means I need at least two read-throughs to do my best job, one to proofread, the other to edit for broader issues like characterization, pacing, consistency, etc. If I find myself reading for content without getting distracted the first time through, that's a compliment to the author's technical prowess.
Sometimes the writer won't agree with your suggestions on the broader issues (and they should always be suggestions; see above note about personal preference vs. actual rules). This is okay. The beta is never responsible for the final form of a story. It's up to the writer to participate actively in the process of making their story as good as possible. They can and should pester you for explanations if they don't understand, or for feedback on a particular topic if you're not giving it. If they take a back seat and blindly do everything you say without understanding it, or if they argue and/or blow you off and do whatever they want even if you were right, there's nothing you can do about it and it's not your fault.
You probably already knew or suspected a lot of that, but I hope I've said some things that help. I'll keep finishing the full workshop on my radar, but I can't promise it'll happen anytime soon.
~Neshomeh