The main scene that shows this sort of corruption is the one in which Gatsby gets pulled over for speeding by a motorcycle police officer. This happens in Chapter 4 as Gatsby and Nick are driving in toward New York City.
The police officer pulls Gatsby over. But then Gatsby shows the officer something from his wallet -- a white card. After that, the police officer starts to act all deferential and respectful. He apologizes to Gatsby for pulling him over. This is because the commissioner of police owes Gatsby because Gatsby has done him a favor. This shows that the high officials and the police can be bought.