After Emmeline teaches the baby to swim, they go swimming together. In the underwater shots they have no clothes on but in a close-up of Emmeline, a little piece of clothing is visible.
When Emmeline walks in the water she accidentally steps on a fish and gets sick. The fish that the movie shows is called Stone Fish and in fact if you step on one the venom will cause excruciating pain and also shock, paralysis, tissue death and if not treated within few hours also death. Emmeline doesn't seem to suffer from any of these symptoms and it seems it takes some time until Richard finds her.
When Richard goes fishing from the boat and his catch is attacked by sharks, tearing the line from his hands, a rope can clearly be seen dragging the first (presumably dead/fake) shark through the water
The Blue Lagoon (1908) was written by Irish-born author Henry De Vere Stacpoole. The novel was adapted for the screen by American screenwriter Douglas Day Stewart.