At the point where Batman and Robin are going to investigate the suspicious buoy, they drive the Bat-Boat and talk about the disappeared ship and commodore Schmidlapp. When Batman tells Robin to watch out for suspicious ships, look closely at the sea behind Batman. If you watch carefully, you can see a motorboat go behind him. Soon after this Robin looks at the dashboard of the Bat-Boat (obviously checking the radar) and says: "It looks like we've got the whole ocean for ourselves"!

Either the radar has a very short range, or is malfunctioning ;-)