It is always nice to have a chance to clean up before the police come over. Typically it is something like, “Open up, Police! … OPEN UP! POLICE! *smash*” or “We had a call about your party from one of the neighbors. Keep the noise down.” This time, we know they are coming.
American Beauty Man is being excessively creepy and exhibiting stalker-like traits. While he has not done anything illegal (yet!), the nice lady at the police station front desk suggested they take a report when Meta_Kate asked about self defense courses. This ends up being good for several reasons. First, if something truly bad were to happen, they would be more apt to believe it if they had some previous reports on file. Second, if he sees the cops coming to the house, hanging out for a while (while the report is taken), then leave, it might spook him enough to calm down a bit–plus he would not know why they were there, so that works out kind of nicely in a non-confrontational sort of way. Third, they will be able to look up his address in their database and know if he has a history (sex offender or otherwise).