Corrected entry: At the start of the movie, when the ship stops and looks in the boat and find the two people and the baby, the captain of the ship asks whether they are alive or not, and the mate says the adults in the small boat are dead, but the child is alive. But at the end of the Blue Lagoon, the mate answers the captain with 'no sir, they are just sleeping.'
Corrected entry: They arrive on the island, and 10 years later we can see them washing themselves with what is clearly soap.
Correction: Back then a lady might very well have known how to make soap with animal fat, ashes or some plant ingredients. Store bought soap was often an expensive luxury. She simply taught the children how to make it.
Grumpy Scot
Correction: This was the mate's way of breaking the news gently to the captain, who is Richard's father and Em's uncle. Also, a continuation of the 'go to sleep berries' theme.