Factual error: At the end of the film, SGT Angel gets into his Police car Subaru Impreza, and on the bonnet it has the writing 'Sandford Constabulary'. This is incorrect, it would in fact be 'Gloucestershire Constabulary' as established at the start of the film that Sandford is in Gloucestershire. A Constabulary is always named after the County, never after a tiny village within that County.
Factual error: Somehow, after being visibly shot directly, at least 6 times, the glass or plastic window of the deli case does not shatter, with powerful shotgun bullets merely ricocheting off glass. [Originally, Wright wanted the glass at the deli counter to shatter during the supermarket shoot-out. However, the production decided it would be too expensive to replace because it was curved glass. To explain why the glass does not shatter, Wright included sounds of bullets ricocheting off bulletproof glass, presuming Skinner had planned ahead and made his deli out of bulletproof glass just in case the fuzz came after him. However, when the cops rammed the shopping carts into the deli counter at the end of the scene, it broke the glass anyway.]
Factual error: PC Angel's collar number is initially HF 777. Whilst a borough code of HF doesn't actually exist there would be a borough code for the Metropolitan Police as it is big enough to warrant one. I'll guess the HF to be for Hot Fuzz? Once PC Angel is promoted to sergeant and also transferred to Sandford his collar number changes to SF 777. Not only would the borough code not be required in the much smaller Sandford, but SF is a Metropolitan borough code for Finchley. The number would also change from 777. Three digit numbers are reserved for constables whilst sergeants would have either a one or two digit number, as in Martin Freeman's HF 90. The twin sergeants, Turner, both have collar number SF 101, when they should have different one or two digit numbers, likewise sergeant Fisher who has SF 137 and the later promoted sergeant Butterman, SF 128. It appears that the format of these collar codes is left to the discretion of each constabulary but the number of digits denoting rank seems to be uniformly accepted throughout the UK.
Factual error: Angel says he went to Canterbury University. It's actually called the University of Kent or the University of Kent at Canterbury, but never Canterbury University. Canterbury Christ Church University, Canterbury's other university, only became a university in 2005, after Angel is likely to have ceased being a student.