Sir Edmund Hillary from New Zealand (whom Race mentions) was the first man (along with Tenzing Norgay of Nepal) to reach the top of Mt. Everest on May 29, 1953.
Animators who couldn't follow in the style of creator Doug Wildey had to be borrowed from sister productions of The Flintstones (1960) and The Yogi Bear Show (1961) to meet Jonny Quest production deadlines. This is why the Yeti sometimes look truly frightening and sometimes look like roly-poly inhabitants of Jellystone Park (Yogi Bear's domain).
In this episode, Race comments that Sir Edmund Hilary proved that Yeti don't exist. This is not entirely accurate. In 1960, Sir Edmund did attempt to debunk the Yeti by bringing a Yeti "scalp" and showing that it was actually made from the hide of the serow (a goat-like animal). However a number of cultural experts already knew that Sherpas of the region made ceremonial caps to resemble the Yeti and were not really passed off as authentic. So while Sir Edmund "proved" that the Yeti scalp was not authentic, he did not disprove the existence of the Yeti as a species. The existence of the Yeti is still debatable even today as sightings continue.
The shot of the monastery at the beginning of the episode is also the same shot used in the intro to the Adult Swim show Aqua Teen Hunger Force.