"The Right Profile" is about Montgomery Clift, one of the great trinity of American actors who blazed upon audiences from the silver screen in the early 50's (Clift actually began his career in the 40's) - the others being Brando and James Dean. The song refers to how Clift, following a horrific car crash was to be photographed only on the right, "Shoot his right profile", as this was the side that most closely resembled his pre-accident features. If you know Clift's work, the accident didn't disfigure him, it merely made a beautiful man more ordinary.
He was also a troubled man, having to deal with suppressing his homosexuality in America of the 40's and 50's, plus doing so under the microscope of homophobic Hollywood. Add onto this: self loathing, addictions to pills and booze (only exacerbated by the abuse of painkillers after the car crash), and you have the makings of a great biography (Patricia Bosworth wrote one), a great film (not sure if that was done or not), or a great song, done by The Clash... off of "London Calling", here it is.
+ The Right Profile