When Egghead writes the letter, it reads: "To Bar None Ranch, Wahoo, Wyoming." When the cowboy receives the letter, the "To" and all of the punctuation are missing.
The calendar on Egghead's wall shows June, 1937 beginning on a Monday. In 1937, June began on a Tuesday.
There are Saguaro Cactus at the Bar None Ranch in Wahoo, Wyoming. But Saguaros do not grow anywhere in Wyoming. They are only located in the Sonoran Desert, which is located in Southern Arizona and northern Mexico.