"The Right Stuff" certainly had its cringe-worthy moments, especially the broad stereotypes of German rocket engineers. ("Just....do it in ze suit!")
But I just realized I had tossed it into the same mental hash bucket as Michener's "Space", which was considerably worse. I gagged when Michael York's parody of von Braun has a "Eureka!" moment when he suddenly invents the concept of rocket staging out of whole cloth to a dumbstruck room of fellow rocket scientists. The idea was already at least 500 years old by that time, and the theoretical details had already been extensively worked out by Tsiolkovsky, Goddard and Oberth, among others.