Show the badge to the thief. No impression at all.
Go to the entrance to convention and talk to Murray. Ask him to show his badge and give him the toy one.
Show the police badge to thief. Unfortunately, someone stole the ring.
Go to pub, go to the alley (through the back door) and talk with the bum. Use the water gun with the bum. Take the ring from bum's finger. Sally calls, so go inside the pub (by main door), close to the table, where she's sitting and talk to her.
For ending the fourth chapter you'll unlock the achievement 'Day 5' (on the beginning of next chapter).