Deliberate mistake: When Sidney is typing the message to the police, you can see that there are red lights flashing, which must mean the police are there, 5 seconds after she types. Obviously deliberately done for the humor. (00:29:30 - 00:30:25)
Suggested correction: Contrary to what the entry says, I don't see police lights flashing as she types, nor when she talks to Billy. I do agree that still it's barely a minute before the police arrive in full force on the scene and it's pretty ridiculous (although I am not sure it's deliberate humour).
There's a time skip between Sidney encountering Dewey at the front door and Billy being arrested. It's plausible Tatum had sent Dewey to check on Sidney knowing she was going to be late, and so he arrived before the rest of the authorities. Billy did not chase after Sidney and likely reacted calmly to Dewey to look as innocent as he could, he wouldn't necessarily have been arrested right away.
