Other mistake: On his own computer, Sean looks up his son's file, which states the boy died immediately and his date of death was September 9th, 1991. When Eve and Castor (as Sean Archer) are at the cemetery, the date of death on the headstone is September 24th, 1991. (00:21:15 - 01:14:50)
Other mistake: When Troy (as Archer) goes to defuse the bomb, the #1 key lights up before he even presses it.
Other mistake: At the prison, when Sean Archer (as Castor Troy) is talking to Pollux Troy to find out where the bomb is, Pollux hands him a cigarette. Never lighting the cigarette, in the next shot the cigarette is lit and he is smoking from it.
Other mistake: In the scene where Archer (as Troy) escapes with Ivan Dubov we see their tracking blips still moving on the tracking monitor after their tracking boots have been removed. (01:06:35)
Other mistake: When Archer (as Troy) and Dubov are fighting with the guards prior to Archer escaping, we see two guards looking at a computer screen which has several prisoners names registered on it, including Pollux Troy's name. Pollux has already been released from the prison by this stage, so his name should have been removed from the prison's computer system. (01:06:50)
Chosen answer: It's obvious that enough time hasn't passed for a trial of such magnitude to take place, meaning that the brothers have been remanded in custody to await trial. They should have been arraigned but we don't see that onscreen.