The locker room at the school has a passive Infra red detector clearly visible over one of the doors more recently used for intruder alarm systems. This type of device would not have been available until the early 1990s.
In the montage scene in the library, at least three books, Michael Burleigh's "The Third Reich" (2001), Alan Bullock's "Hitler and Stalin: Parallel Lives" (1991), and John Guy's "Tudor England" (1988) are visible, neither of which had been published in 1983/84 when the film was set.
The lollipop lady that reports Hector to the headmaster carries a sign that carries the international symbol for children, which has only recently started replacing the old sign that stated "STOP CHILDREN" - which would have been the sign used in 1983.
When Posner and Hector are discussing the poem "Drummer Hodge" by Thomas Hardy, Posner references Rupert Brooke's poem "The Soldier" by mentioning the line "There's some corner of a foreign field... in that dust a richer dust concealed." The line is actually "in that rich earth a richer dust concealed."