I mean the idea of the CR is to sort out disputes on FSE, be a middle man between community and moderators (such as suggesting new language boards if someone approaches them and they deem it having potential to be used or new functionality on the forums). On top of that they can do some minor level moderating such as snipping posts, but can't warn anyone.
They also normally get involved in any boards in the admin section such as ban suggestions, functionality suggestions and board requests.
Though in all fairness since Chicken's first few weeks I haven't seen him on FSE much.