In The Green Mile, although there are some minor changes between the novel and the film's script, I think Stephen King's intent is preserved in the movie.
There are minor changes that do not affect the story's outcome in film.
One of the trademarks of Stephen King's writing [his]... moral earnestness... The Green Mile's...purpose is to kindle the reader's [viewers] outrage at the inhumanity and capriciousness of the death penalty.
In both the movie and film, the narrator is:
Paul Edgecombe [who]...combines a powerful empathy with the condemned men with a tendency to ponder the ethical and spiritual implications of events. Paul's compelling voice is the novel's moral center.
Perhaps the major difference is found in the character of John Coffey:
In the novel there is strong evidence to suggest John Coffey is innocent. This is interpreted by Paul Edgecomb the narrator. The confusion of the tracking dogs is a major part of this. In the movie this is transformed into the scene where John Coffey grabs Paul Edgecomb's hand and transfers the image from William Wharton, the real killer, to Paul.
However, the result is the same: that the audience believes that John is innocent.
In studying the issue of capital punishment, we see in both versions men who are evil personified and deserve to die, and still others where the decision is not clearly black and white.
It would seem that William "Billy the Kid" Wharton is someone who should have been executed, and he is in a way, but not in the chair. Percy Wetmore is vicious and sadistic: he, too, is punished, but not with physical death. However, with John Coffey, the audience knows, both in the book and the film, that there is more to this man than meets the eye. He is a gentle spirit:
The imagery surrounding Coffey is, however, the most explicitly Christ-like. Next to nothing is known of Jesus before His thirties, when He began His public ministry. Similarly, Paul can find no clues to Coffey's life before his disastrous attempt to heal the Detterick twins, except what can be deduced from the scars that cover his body. Coffey, like Jesus, heals, exorcises demons, and brings the dead back to life. Coffey heals Paul's urinary infection, draws the demon (...a brain tumor) out of Melinda, and brings Mr. Jingles back from the dead after Percy has crushed the mouse.
These perceptions are present in both versions. Paul Edgecombe and Brutus "Brutal" Howell (and others) are haunted by the execution of John Coffey. The death of this unusual man drives home the idea that capital punishment, through the judicial system, makes mistakes that can never be corrected.
In the novel and the film, King allows the audience to experience the pure evil of some men, and the puzzling goodness in others. Murder is murder, but the novel and the movie make us look at capital punishment in a [then] twentieth-century context, where there are many more shades of grey.
The changes between the novel and the film still carry the weight of King's message. He gives his audience reason to ponder the wisdom of men, and to see the irony of goodness in the convicted (Coffey) and evil in the establishment (Wetmore). Long after the Depression is over, King's message against the use of capital punishment is still relevant, and loses nothing between paper and film.