There were two incredibly close calls on the set, both of which occurred during scenes with the family playing in the water. First, when the father takes a swing to try to change vines like the monkeys, he misses and falls into the water. John Mills revealed that his foot just missed a sharp, jagged rock under the water that no one had known about. Then there was the scene with Francis playing in the ocean with Rocky the baby elephant. At one point, Kevin Corcoran fell under, and the elephant's foot ended up right on his face. But, by some lucky chance, the underwater current was so strong that it prevented the foot from pressing down, and thus Kevin from getting hurt.
When the studio acquired the rights to Johann David Wyss' novel, they essentially junked about 90% of it. Ken Annakin and his technicians brainstormed all the things they'd like to have seen in a desert island picture, storyboarded their wishlist and then handed it all over to screenwriter Lowell Hawley.
The Disney Studios bought up the rights to the 1940 version produced and distributed by RKO, then Walt Disney confiscated all known prints of RKO Radio Pictures version so there wouldn't be comparisons to the Disney remake.
During construction of the Robinson's tree house residence, Father Robinson shows Mother Robinson the stairs to their bedroom saying, "This is your own circular stairway"; perhaps a reference to Dorothy McGuire's popular 1945 film The Spiral Staircase, as the stairway is obviously 'straight' and not circular.