We have problems with some review pools not responding to claim a participant slot in reviews. When the reviews are created by non-admin users, they don't have any way of contacting the members of the review pool that are failing to claim the slot(s) since they have no way to determine who's even assigned to the review pool. Only an administrator can determine review pool membership, and only by opening the Admin settings and examining the group directly.
Ideally the review pool name in the participant list would be a hyperlink to the page listing membership in that group. Though not strictly needed, it might also be useful to have a place where unprivileged users could look at the membership of all review pool enabled groups without having to add a review pool to a review simply to access the link to the membership page.
Since some users may want review pool membership to be opaque, it might be necessary to add it as an extra option on each group to indicate whether a review pool enabled group should have visible membership.