If nothing else, I think Anonymous Monks should not be allowed to see the Worst Nodes list. I'm not sure what level is a good starting point, but I would agree it needs to be at least level two. Level 5: Beadle
comes to mind since that's when a user can have a homenode and can ask categorized questions. On the other hand, level 5 seems a little too high.
I really don't like the idea of further restricing some nodes to just certain groups or levels. However, if it were going to be done I'd set the bar much lower: either Level 5: Beadle, Friar (level 10), or at worst to Saints in our Book. But as I said, I'd prefer no further restrictions.
Update: fixed grammar and broken id:// link; slight rewording.