Revealing mistake: Take a good look at the crowd of backpackers waiting outside the office in which Richard just has been questioned by the police. They are the same people that later in the movie are welcoming Richard to their happy, secret paradise island community.
When Richard and Francoise are making love on the beach. They begin kissing deep under the water and continue all the way to the top. When they reach the surface they can stand up in the water which appears to be waist-level.