The character Roger Thornhill (played by William Devane) is clearly a reference to Cary Grant's character, Roger O. Thornhill in Alfred Hitchcock's North by Northwest (1959).
The actual name of the Chimpanzee that was suborbitally launched, was "Ham" (an acronym which stands for Holloman Aerospace Medical Center). He was given that name upon his successful return to Earth.
This movie shares many commonalities with Philip Kaufman's The Right Stuff, including the problems with designing the Mercury capsule and the presence of Mac the chimp and Alan Shepherd.
Parts of the movie were filmed at Cocoa Beach Jr Sr Hight School in Cocoa Beach Florida.