They should have played guessing games

To prove that Sam Wheat was in the area they should ask Molly to go to the bathroom alone, write down a number 0-1000 and then show the empty room what it was, then Oda Mae can get the answer from Sam, repeat as many times as you want until she is convinced and even get Molly to write out a letter of random gibberish that Oda Mae can repeat word for word

Then bring everyone to the police station and play that game on the sarcastic bitch police officer