What is the film saying about madness and mental institutions?

The film is very close to the book in terms of thematic content. The question actually demands some depth. To a large extent, these institutions perpetuate the mental problems rather than treat them. In the case of Chief Bromden, for instance, the Indian has convinced others—maybe even himself—that he is deaf and dumb. This chosen handicap dictates the conditions of even the most mundane moments of his life. Meanwhile, for the rest of the inmates, in group therapy sessions Nurse Ratched uses the power of suggestion to expose their deepest insecurities. Ratched uses these  insecurities are used against each patient which only compounds their issues.  We see over and over that belief in a particular ailment seems to induce it. Specifically, in the case of electroshock therapy (EST), given to disturbed patients whenever they misbehave, most of them succumb and find themselves changed negatively by the experience. Chief Bromden, in particular, says that fighting EST was not an option: the fog simply envelops you and warps your brain. Some people have genuine medical conditions. Ratched herself cannot wish away her large bosom. As for McMurphy, he cannot withstand Ratched's final tool of punishment, the actual removal of part of his brain.