Continuity mistake: When Angel asks his superior why everyone is eating chocolate cake, behind Angel you can see Danny with a literal few crumbs left on the plate. When the Sergeant replies to Angel and Danny looks up smiling, you can see there is now a lot more cake on the plate.
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.
Suggested correction: While there's a lot of details listed in the mistake, the rank of sergeant is denoted by 1, 2, or 3 digit numbers and constables are denoted by 3 or 4 digit numbers (unless of course there are too many officers and larger numbers are needed).
Suggested correction: Police forces do not routinely denote rank by number of digits. I'm sure some forces do, however, I have personally worked in two police forces where this was not the case.
Visible crew/equipment: When the police are storming the local Somerfield shop, after pushing the trolleys into the butchers, they are attacked by others of the shops staff who are throwing fruit. In one close up shot of the fruit being thrown if you look carefully at the pineapple as it's in the air there is a white part on the bottom. This suggests that the fruit being thrown are actually plastic. Slow motion is useful to see this but not required.
Continuity mistake: The shoplifter at the station constantly changes stance depending on the camera angle; he leans against the wall, then slouches forward.
Other mistake: Sergeant Fisher is never seen wearing any rank insignia. He therefore appears to be an ordinary PC.
Continuity mistake: When Michael (the 'yarp' guy) has been knocked out by Angel, Danny appears and gives Angel his notepad. Angel then turns to leave twice.
Continuity mistake: When Martin Blower and Eve Draper get pulled over for speeding by Angel and Danny, Eve's arm alternates between being on the door frame and being by her side at the start of the conversation between Angel and Martin Blower.
Revealing mistake: When Michael is unconscious in the freezer after the fight with Angel in the supermarket, there is a close-up of his face and you can see his real teeth behind the prosthetic ones.
Continuity mistake: When Angel, Danny and the Andies are running with the trolleys to the butchers in Somerfield, two others give cover fire and appear in the isle behind Angel and Danny. Camera cuts and they appear again.
Revealing mistake: The shot of Nicholas Angel jumping into the skip is a stuntman with a rather vividly dyed wig.
Audio problem: When SGT Angel is at the train station with his Japanese Piece Lily and is waiting on the bench, we see a British Rail Class 165 leaving, however the speed the train is going at is too slow for the matching traction sounds (the sound of the train going over gaps in the rails). Also the rear of the train does not match a Chiltern Railways 165, it looks as if it has been edited (although the number reads 165007). Later on, we see Angel almost dropping off to sleep and a fast train comes in and blows the horn, the horn sounded does not match the horn that would come from this type of train, it sounds more of what would come from an EMU version (possibly 365 or 465 Networker).
Other mistake: When Sgt. Angel meets Joyce Cooper at the hotel, she is making a crossword puzzle. She said "Fascist" and then read the definition, but that word is not 7 across as she says, but 14 down.
Visible crew/equipment: After Frank shoots the light thing on the ceiling and he gets away, just about when Nicholas says "He'll come round" and the camera is aiming down where Frank got away, look at the bottom half on the screen and you can see someone's/something's shadow moving.