In a scene set in 1984, Joe and his family are seen watching the government TV advert "AIDS: Don't die of ignorance". The slogan was first used in November 1986 and the advert was first shown in January 1987.
When they dial the number for the town in Wales having used the phone book they dial 01.....In the early-'80s all area codes would have not have had a 1 as the second number, they were 0823 not 01823 etc. At that time, 01 was the long distance (STD - Subscriber Trunk Dialling) code for London.
In the final scene shot outside the Houses of Parliament and set in the late 1980s, Portcullis House is shown in the background. The building was not commissioned until 1992 and only opened in 2001. Also, the Terrace of the Commons is shown in the background of the same scene with marques on it. These would not have been installed in the 1980s and were a later addition.
In the film, the LGSM group chooses a pit in South Wales randomly. In real life, the group had deliberately chosen the South Wales area as it disagreed with the NUM leader Arthur Scargill's funneling of donations to the most militant mining areas of Kent and Yorkshire, which left South Wales neglected.
The button Mark gives Joe when they meet after watching the miners returning to work in Onllwyn says "I am (discretely) gay". This is a common error, but it should be "discreetly" meaning cautiously or with tact; "discrete" means separate or distinct. However, it could be a copy of a vintage button, in which case the error is on the part of the original designer of the button, not the filmmakers.