What they do at club_joss is as follows: the mod posts an "assignment" post with a link to the selected story, says something like "You all have an [amount of time] to read this!" Then, [an amount of time later], the mod posts a "discussion" post, and the members all talk about their opinions of the fic in the comments.
The idea isn't entirely based in academia, so anyone could participate-- someone could read a story and simply review something to the effect of "This is good, and I especially liked your Wakaba characterization!" or "The dialogue you used for Saionji was very funny!" or maybe even "I don't understand why Touga was wearing a skirt here. Am I missing some critical symbolism?"
Writers could receive constructive criticism or rave reviews (and possibly even explain their writing processes!), and readers could broaden their horizons or share cool and/or obscure fanfiction.
Is anyone interested in participating in something like this? If so, we should sort out a few key issues: are we going to include drabbles/poetry/drabble sets? How frequently should we do this-- weekly, bi-weekly, or in some other period of time? And, if this idea garners enough interest, should I create a separate community just for this purpose? ...Et cetera!
(Obviously, I am willing to help with any organization that is needed.)