Lockwood was killed in action with the York and Lancaster Regiment. They were disbanded in 1968.
Hector's motorcycle has a front number plate. By 1983 they had been obsolete by around a decade.
The motorcycle is a Velocette from 1955 and would have had a number plate at the front. The law was changed in 1973 but motorcycles registered before that were allowed to keep the front number plate.
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.
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 which had not been published in 1983/84 when the film was set.
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.
The first time we see Hector giving a lift to one of the pupils on his motorbike, they drive past a house with a satellite dish on the wall. Satellite TV did not exist in the UK in 1983.
In the staff room when Hector says 'French Kiss' to the games master, he is holding a copy of the Racing Post. The Racing Post wasn't launched until 1986, three years after the year the film was set.
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."