Sun protection creams and lotions were just being developed at the time of this short. They came about from the products needed during WW2, when the harsh effects of prolonged sun exposure were realized. Tom uses some of these early items here, such as zinc oxide (still in use in the present day).
The aftermath of Tom's encounter with the rusty anchor might be viewed as racially inappropriate in the present day, as it mimics the actual cultural practices of the African (Ndebele) and Asian (Kayan Lahwi) peoples, who both use large metal jewelry rings to elongate their women's necks.
While the mer mouse is just a fanta sea, the other critters encountered (sea stars, sea horses, a swordfish, a giant octopus, and more) are all actual inhabitants of the briny deep.