The obelisk in this episode, constructed at Franklin Lake in the Franklin Canyon Reservoir above Beverly Hills, was erected in the same spot where Opie Taylor throws a rock into the lake during the opening credits of The Andy Griffith Show (1960).
Paradise Syndrome - though not officially recognized as a mental condition by psychologists - is a term conferred upon those who feel dissatisfied despite having achieved all their dreams. Here it is used merely to describe someone who is overworked and needing a break - whether ostensibly Captain Kirk or obliquely series creator Gene Roddenberry.
The Native Americans depicted display none of the cultural elements of the tribes mentioned (Navajo, Delaware, Mohican). The houses are tipis, used by plains peoples. The clothing bears no resemblance to actual Native American clothes, and the names of the characters match no Native naming styles. Also, the Navajo were not peaceful. They were very fierce warriors, as were the Mohican. The Delaware were not called "Delaware," but rather, were the Lenne Lenape.
After living on the planet Kirk's sideburns lose their distinctive pointed ends and become squared off. This was done to emphasize the passage of time and to show Kirk was becoming assimilated to his new life.