Arnold told the detectives that he and his grandfather left the mini-golf course at 8am on the dot.

This is impossible because… if the game started at 07:00 or even anytime after 07:00, Alfred would not have been ready to leave the competition by 8am.

Mogau knew that the winner took 57 minutes to finish the game and that the runner ups finished no less than 5 minutes after him. As one of the last people to finish, Alfred would not have been ready to leave until much after 8am.

And we know the game had to start between 07:00 and 08:30 because that is when Ken took off work to go see it.

This means Arnold accidentally contradicted the timeline of real events and so he inadvertently confessed!