When the hold-up first occurs, Sid James is clearly very drunk indeed and sitting in his office, but mere minutes later he his driving a cab to intercept the robbers with no sign whatsoever of being under the influence of alcohol at all.
At the start of the film Smiley backs into the main gates causing considerable damage. However, when Charlie is training the lads in his yard later in the day if you look in the background you can see that the gates are no longer damaged.
When Sally throws the crockery at Ted in the cafe she picks up 2 items and throws them 1 at a time yet when Ted is running out of the cafe multiple items of crockery come flying through the door behind him. It would not be possible for 1 person to throw that many items of crockery in such a short space of time.
When Sarge tells Allbright to follow the robbers and Allbright remarks on how the union will react to this, Sarge's mouth remains shut when we hear the noise used to cover the rude word in his response.
Many, if not most, of the Glamcabs only have two doors, which would make them unsuitable as taxicabs. All scenes involving passengers only used the four-door cabs.
Despite being on a 'No through road' to the heath with only one way in or out, and 'Peg1' being one of the first cabs to leave the gathering on the heath before being run off the road by Hawtrey on his moped, no other cab or Police car passes them and none are found when Charles Hawtrey is sent to find and stop one at the end of the film.