When Nathan is electrocuted in the first part of the film and his implant is switched off. It is behind his right ear. Though when the group venture out and he stops to complain about carrying the battery it has moved to behind his left ear.
Just after Kate (Gillian Anderson) is seen riding the horse on the beach, the kids on their obtained vehicles can be seen catching her up on the road in the background. Initially, the Jeep is ahead of the quad bikes, but after the jump cut, the quads are in front.
When Nathan finds the case of Zippo classic wind proof lighters in the train museum shop, he immediately tests it out and strikes a flame. This is not possible as Zippo lighters are shipped without fuel, one must add fuel after purchasing the lighter.
Danny is a Royal Air Force pilot but wears the rank of a flight sergeant (aircrew) which is not a rank that pilot aircraft. Only commissioned officers are Royal Air Force pilots and flight sergeant (aircrew) is a non-commissioned rank (NCO), albeit one that works on aircraft (such as a loadmaster). There is a possibility that he is wearing someone else's flying suit but any Royal Air Force officer would immediately remove the incorrect rank from it. It was only during the second World War that NCOs in the rank of sergeant, flight sergeant and Warrant Officer would be pilots.
When everyone is celebrating their victory in the final scene, some actors have no implants and others do. However, with the destruction of the robots, the electronic implants are non functioning. One of the extras in the celebration victory at the end (at around 1h 21 mins), forgot to turn off his implant battery and it can be seen briefly flashing.
When Smythe (Ben Kingsley) is shot and falls over a wall an onto a pile of tarps/garbage, a safety cable is briefly seen immediately when the POV changes from the fall to him getting up.
The vast majority of the outside locations filmed show evidence of a thriving civil service (clean streets, bins emptied, infrastructure maintained). If no-one is allowed outside, why are the streetlights still turned on at night?
If the world is taken over by robots, why the main protagonists are searching for files, and why deceased people are marked by crossing their photographs by read scotch tape? A database would be more reasonable way to go, especially if there are no computers (at least none were shown) and robots seem to have installed computer to brain interface implants to everyone.