In one long shot of some houses small black Sky TV satellite dishes are visible. Sky TV did not begin broadcasting until the late 1980s, and this style of satellite dish was not rolled out until the launch of Sky Digital in the late 1990s.
The takeaway that Shaun passes, early on in the film, has a telephone number starting with area code 0115 - this area code did not come into effect until the early 1990's, 10 years after the film is set.
When Shaun first meets with Woody, Milky and the other skinheads, in the tunnel after the fight at Shaun's school, you can clearly see that they've written 'Screwdriver' with spray-paint, but the group it refers to is spelt 'Skrewdriver'.
When Combo was explaining the level of unemployment in the UK at the time (1983), he referred to a figure of 3½ million. Although unemployment figures in the early 1980s were staggering this figure was not reached until 1986.