I too run some groups on Facebook -- including The Ask Dave Taylor fan club, which you are a fan of, right? :-) -- and know exactly what you mean. If it's a well-meaning but misplaced posting then I usually just delete it without any sort of penalty or block, but if it's someone who posts stuff in the group that's just annoying, inappropriate, of an overly political nature, or just plain rude, then I do consider blocking them.

Your timing is good because just a few days ago I had a situation of this nature arise in the ADT Fan Club and captured the sequence I took to not only remove the posting from the group wall, but also block this participant and report them as a spammer to Facebook itself. Now, what Facebook does with these reports I don't know, but I certainly think that reporting them is always better than not reporting them...

Anyway, there I was checking my group and I saw the following posting:

Suhaimi might be a lovely chap, but this kind of posting is wayyy off the mark in my Facebook group and, frankly, given that I write about how to do stuff like this, a doubly dumb move because now he's forever marked as a spammer here on my blog. Ooops!

To just delete the post, I can move my cursor to the top right of the invisible box that his posting's within, at which point an "X" magically shows up. Click on it and here are my basic options:

Instead of just "Remove Post", however, I'm going to "Report as Abuse", which produces the following explanatory window:

Note that one option is related to bullying or rude comments about you that might appear. If you have kids, this is a good one to tell them about, because Facebook does take online bullying (aka "cyberbulling") seriously. Still, that's not what we want. We just want to mark this as "Spam or scam" and click "Continue"...

At this point I can opt to send a message to Suhaimi but with a posting like this, I'm not going to impact his strategy of spamming Facebook groups, so instead I opt to block him from the group and report him to Facebook. Here's what those look like:

One more click of the "Continue" button and it's a fait accompli:

Note that as the group manager you should definitely set things up so that Facebook emails you copies of whatever's posted to your Facebook group by going to "Edit Page" (top right button on your group's home page) and looking at the settings under "Your Settings".