While watching this today on Metv I noticed the whale had the same concern the "Free Willy" whale had many years later. That is, that the top fin was drooping.
As I recall the explanation given then was that Willy was a whale kept penned up thus causing this concern.
Perhaps no one knew what caused this at the time of filming Namu, the Killer Whale.
Dorsal fin collapse is characteristic of captive male orcas, and some females as well. It happens in 100% of captive males, and some captive females. Alternatively, less than 1% of the wild orca population worldwide experienced dorsal fin collapse - and it is usually due to injury or illness.
The most wildly accepted theory is water pressure and gravity. Wild orcas spend little time at the surface, mostly in deep water where water pressure helps keep their dorsal fins straight. In captivity, orcas are trained to spend a lot more time at the surface for feeding, performances, training, etc and are also kept in pools that are much shallower than the ocean they would be living in in the wild. The result is gravity acting on the dorsal fin, causing it to flop over, and the shallower water doesn't have enough pressure to counteract the force of gravity.
Namu, the orca in this film, was kept in shallow sea pens from 1965 to 1966 before he died due to a bacterial infection (Clostridium Perfringens) which lead to drowning. While this wasn't enough time exposed to gravity and low water pressure to cause his dorsal fin to collapse fully, it was in the beginning stages of collapse. During the time Namu was in captivity, little was known about orcas - no male orca had been kept in captivity long enough for his dorsal fin to completely collapse. The issue was unknown at that time.