I can't imagine what they can do. The laws limit where convicted pedophiles can live and work, and publish their names online. What more are you thinking the police would be able to do? Since he's living with his mother I assume he is probably not able to work at this time (who would hire him, after all.) Where could they force him to move to? Unless the taxpayers are going to pay for his keep (I'm thinking NO on that one!)
Being informed is the best approach. I know the principal of our grade school watches the sex offender lists closely and we have both school and community email lists (formal and informal) where people share information about any strange goings-on. If you don't already have one, start a block/neighborhood email - nothing fancy, just a list of names - where you can share information on all sorts of things including, unfortunately, sometimes news about weirdos.
ETA - you might also talk to the local schools or PTOs or library about sponsoring a kidpower or similar event for parents. http://www.kidpower.org/