Wolfe definitely keeps the tale interesting. He focuses on the personal, rather than the technical and administrative, aspects of the Mercury space program and the first seven astronauts involved. He follows the seven through their early careers, mostly as test pilots, through each of their turns in a Mercury capsule.
The most remarkable part of the story is the connection Wolfe makes between fighter jet pilots and astronauts. Having grown up in the NASA age, I did not know that the Air Force had a competing rocket program (a program that managed to send pilots several miles into space and then have them actually land the aircraft back on earth) before it was scuttled in favor of NASA's moon missions.
The only drawback of the book is Wolfe's Gonzo journalism style, which much have been refreshing and bold back in 1979. Now, the hipper-than-thou tone is a little tired and can get exasperating.