Christie is wearing a police uniform when Muriel Eady comes to the house in the opening scenes but he had already long left the police by this time. Muriel would have known this as she and Christie met when they both worked for the same employer.
The position of the manhole cover changes from shot to shot when the police lift its lid after Evans' "confession" - first it is seen (as it was in real life) in the middle of the road opposite No.10 with the front door to the house closed, but in the next close-up shot we see it being lifted up from a position in front of a bay window from a house further down the street, with the front door of (supposedly) No.10 open
In the Bar scene where Beryl and Tim agree to have the abortion done, Tim is seen drinking from an almost full glass of beer, then when the camera switches, it is almost empty, then it fills back up for the next shot.
At the end of the film where Christie is arrested, the police constable leads him away from Putney Bridge (seen in the background). Putney police station is, in fact in the opposite direction in the Upper Richmond Road. The direction the constable takes Christie in the film would only lead down the river towpath towards Hammersmith.
When Christie is explaining the procedure he's about to perform on Beryl, he says that natural gas contains carbon monoxide, then quotes its formula as CO2 (which is actually carbon dioxide). The correct formula for carbon monoxide is CO. However, the point appears to be to show him for the half-educated conman he is. It's just Christie's character creating an air of "expertise".