What I would do if there was a fight between a moderator and a user and the mod was wrong, and still banned the other player without reason: If the Moderator is Lower Rank: I would find out more about the incident before I did anything. I would then suggest to the person over my head that they should fire the moderator from their position and that they should un-ban the user that was involved.
If the other Moderator was over my head: I would first find out more about the problem. Then I would talk to anyone who is above them. (Admin) I would tell them about the problem and suggest that their rank be taken down a level. I would also let them know that the other user should be un-banned.
If someone had mature content and pictures on their profile I would: First, delete the inappropriate content. Then, I would give him/her a warning. If it was their first warning just log the warning and remember it for future reference. If the user had committed something before they would be suggested for a temporary account freeze, account ban, or IP ban. Depending on the severity of the content and what they had done before.
Let me know if you need anything else.
-Tox