I have named Einar, Crgreathouse and Infinity moderators for various forums of this site. This does not give them any duty but allows them to remove inappropriate messages from the board if they want to. Below each forum you can moderate, you can find a link "Moderate this group" and then options to edit, delete or move the topics which are irrelevant. If you move a topic, you are given the option to leave a shadow of the topic on the forum it was initially posted on.
Generally speaking, I prefer the moderators to remove only the topics which are clearly indecent, vulgar, offending, or irrelevant advertising. Reasonable advertising (mathematically-oriented) is tolerated. For instance, someone posting a message like "I have compiled a thousand of problems on my new website at (link), come check it out !" is acceptable, provided the description is faithful .
You don't need to report anything to me, unless you feel it is necessary.
Concerning the right to delete or ban members, I prefer no member to be banned, but if the spamming is obvious, you can delete the spammers. Avoid banning them though, because banning a member is nothing less then banning an IP, and this may cause problems because large ISP may ban you in return.
Thank you !