When Mac Gopher calls the police, they tell him they can't do anything until Tosh has been missing for twenty-four hours. While familiar to TV and movie viewers, this is a Hollywood invention for dramatic purposes. In a real missing persons case, there is no waiting period before the police can become involved, and investigators encourage reporting a missing person as soon as possible.
When Lola is recaps what they learned from climbing into the mailbox, she notes that the city is making them pay for it. All mailboxes, both public and private, are the property of the U.S. Postal Service, so it would be the federal government requiring them to pay. The city would likely make them pay for the fire department responding, however.
After climbing into the mailbox, Daffy and Lola are seen at her apartment, and their comments indicate the incident lasted only a few minutes. Tampering with the U.S. Mail is a federal felony offense, and in the real world, the U.S. Postal Inspection Service would have been waiting to arrest them. It would have been several hours, minimum, before they were booked, processed, and released on bail.