I suppose it depends on the scale of your "public data hosting service".
If it's something small with maybe a couple hundreds pictures per day flowing in, you can moderate them on your own.
If it's a couple hundred thousands you'll need an amount of human beings sorting the weeds out. It's either a moderator team or users themselves who submit abuse reports.
Which one to go, can be dependent on your budget/financial success of your service as well as on the type of the service. If it's something simple like Rapidshare where one does not see what the other does, the chances that users will see each others content and through this notice and hopefully report unacceptable content are small. If it's something very social like Flickr you can bet on it reports will be flowing in.
I suppose you could automate something but it's almost an impossible task. You can't automatically detect porn. You can't automatically detect images violating copyrights - making footprints of copyrighting material in order to compare them with the uploaded stuff is a real challenge for companies with resources like Rapidshare, Youtube and others. For now this kind of work can effectively be done only by humans.
There are also legal issues to it. In some countries the service owner is not liable for what users contribute (well, if he's cooperative enough to delete certain content at request), in others he will get the charges himself for not having premoderated all the incoming content. Also think of this with regard to whatever and wherever you are going to launch.