Barry Pepper did not receive an Oscar nomination for portraying Mike Norton in The Three Burials of Melquiades Estrada.
In all truth Pepper's approach is what makes not only his performance work but really the film work as a whole. Mike Norton is the man who killed Melquiades Estrada, and one could try to say that he is therefore the villain of the film. Pepper certainly does no portray him as a villain in any respect though, and instead portrays him as a thick headed man who honestly did something very bad simply because he just is not very smart. As strange as it sounds Pepper is honest in his portrayal of Norton's stupidity, he never plays it for laughs, but instead establishes it as really the motivating factor of most of his behavior.
For example when we see Mike actually perform the act of Melquiades Estrada there is no hate in his face or anything remotely similar to that. Instead Pepper shows it as entirely an act of desperation, and he emphasizes the lack of understanding in Mike. Mike jumps too quickly to firing back from a stray bullet, and Pepper shows that this action comes from Mike's lacking skills as a frankly just responsible person let alone boarder guard. When Mike see what he has done, Pepper allows us to actually sympathize with Norton to some degree as he portrays instantly the regrets of Mike over the situation, because his face shows that he honestly did not mean to do it.
Mike troubles grow though when Melquiades Estrada's best friend Pete (Tommy Lee Jones) decides to kidnap Mike to go on an expedition to properly bury his friend. Pepper is excellent in his scenes with Jones by playing the reactions of Mike very much close to the bone. Pepper is very good in simply playing the role as realistically as possible in his reactions to Pete demands of him. He is convincing through the entirety of their journey and Pepper matches the jumbled emotions of Mike all the way. Whether it is his anger at being taken, his pain from the various displeasure he suffers along the way, the regrets he feels when the point of Melquiades death comes up, and most powerfully his fearful uncertainty over what Pete is going to do to him.
Mike seems to undergo a transformation during their journey. It is not that he necessarily that he becomes any smarter exactly, but he seems to slowly break the stupor he seemed to be in at the beginning of the film that really lead him to the unfortunate events that caused Melquiades's death. Pepper is excellent here because he makes Mike's apparent transition something that honestly feels quite natural. He never overplays it nor does he reject the old Mike, as even near the end he still suggest some of the old Mike as he still acts defiantly to Mike. His transition though is made moving by Pepper as he portrays it coming from both a greater understanding of something other than himself as well as in part the psychological and physical trauma he faces through the journey.
This really is not a quiet by nature character, but really the power of Pepper's performance is very much in his face. At the beginning of the film it is a stubborn indistinct expression that he carries mostly that sums of Mike as a person. As the film proceeds though the expression opens up though and he allows us to emphasize with Mike, as he truthfully portrays Mike's changes throughout with particularly strong moments when he opens up fully. These moments are earned, and used perfectly by Pepper as his performance show exactly what Mike is going through. The moment he breaks into tears from a soap opera is extremely well handled he is understated even in the breakdown where Pepper expresses finally an actual understanding of his relationship with his wife.
Pepper builds incredibly though to his final scene where Pete forces him to ask for forgiveness to Melquiades. He starts well though by still showing some of the old Mike as he almost teases Pete. Pepper though is terrific as he genuinely portrays the regrets and sadness Mike does feel for what he has done, even though he pressured Pepper shows what does come is the truth. The only moment better than this in his performance is his final short line asking if Pete will be okay. In this single short sentence Pepper shows us a changed Mike. His expression empathetic, with Mike's wanting to understand know about someone else, and no longer in that stupor. This is an outstanding performance by Barry Pepper creating a fascinating portrait of a stupid man.