Adam suddenly has a different car about halfway through the film.
In the scene in which Adam visits the Klan gathering on the night before the execution the same extra (an older man in a baseball cap) can be seen in adjacent shots both behind Adam and the gang of thugs on the opposite side of the room.
As Adam watches, the digital LED clock in his hotel room changes from 3:59 to 4:00 am, and makes a faint click as it does. Clocks of this kind do not make such sounds.
When Lee (Faye Dunaway) shows Adam (Chris O'Donnell) the photo allegedly of her father at a lynching in Mississippi as a boy, it is actually the iconic photograph of the lynching of Thomas Shipp and Abram Smith in Indiana. The young Sam Cayhill has been edited into the original photograph.
When the defense is asking Packer if Sam was in touch with reality, Adam should have rejected on the grounds that Packer is not an expert in that field. And just because he was a guard for a prison for the same time Sam was there, and only had one incident which was recent, and a trained psychiatrist already said he was not in touch with reality, his statement should not have been relevant.
When Adam meets with Mrs. Kramer to solicit her support (for a stay of execution), she tells him her twins were 5 when they were killed in 1967, "[Adam's] age" when Adam's father committed suicide. Adam was born in 1969 and was 10 when his father killed himself. Mrs. Kramer adds that her sons would "be your age now." They would have been 7 years older than Adam.
Sam Cahall states that the new law allowing him to opt for lethal injection applied only to inmates convicted after 1984. Actually it was just the opposite: Those convicted after 1984 could only have lethal injection. Before 1984 convicts could choose between lethal injection and the gas chamber.
When Adam is giving his argument, he states "Men rea - to do the deed". "Men rea" is the intent portion of a crime. "Actus reaus" is the act.
In the movie, Adam states that his father was "thirty-five years, four months, six days" when he committed suicide - making it impossible to have a son on Adams age.