The only way you break safe harbor is if you know of offending material, eg by a filter or having been alerted to it, and leave that material in place. If you run content filters (such as at the point of upload), then you have to be more careful.
The difference being between after-the-fact moderation and pre-screening. If you pre-screen you take on a greater burden of risk, in terms of copyright holders being able to argue you knew about something and didn't remove it, or should have known.
The safe harbors provided by S512 and S230 are absolute and are not impeded by proactive (or reactive) administration. This is part of their reason for their existence.
(1) a service provider monitoring its service or affirmatively seeking facts indicating infringing activity, except to the extent consistent with a standard technical measure complying with the provisions of subsection (i); or
(2) a service provider gaining access to, removing, or disabling access to material in cases in which such conduct is prohibited by law."
Dude, you desperately need a designated agent. You just aren't under safe harbor at the moment.