When Vincent Moore was presenting his Moose robot to the police chiefs, his hair was closely trim above the forehead. After they rejected his pitch, Vincent went into a washroom and his hair was noticeably longer, as well as his beard being a bit scruffier now.
When Chappie is being taught to speak by Yo-landi at the gang base and Deon arrives in the Mercedes Tetravaal Robotics van, the registration plate on the front reads "FOK OFF GP", in a later shot the plate reads 891TJY GP, yet later when Chappie is taken out to see the real world, the "FOK OFF GP plate is on the grey Volkswagen mini bus that the gang are using and it stays on this van for the rest of the film.
Police vehicles in Johannesburg do not have regular registration plates ending in "GP" (Gauteng Province, the province Johannesburg is in), but rather end in the letter "B". The registration plates for the police vehicles in the movie are "GP" plates.
With hundreds of scout units in the field, the movie starts by making a point of saying that there is a completely secure way of reprogramming them, ensuring that there is no problem with programming in the field. Yet two characters set out to retrieve the single "key" that prevents this from happening and there is not a single camera, security guard, two-person key lock, or even a janitor in the building that houses the lock.
It's pointed out multiple times that Chappie's lifetime is limited to only about five days because his battery is fused into his chassis and can't be replaced, but it's never explained why the battery can't simply be recharged in place.
With only one single physical guard key in existence that is required for reprogramming all of the Scout-type robots, and since it's only needed for reprogramming them and not operating them, Deon would have been extremely careful to have removed it from Chappie after his reprogramming and before his activation.
The helmet for the Moose was described as being a 'neural interface' that allows the operator to control the robot with his/her mind. When Vincent sends the Moose out to kill Chappie and Deon, he's using a HOTAS control system similar to what you'd use to fly a fighter aircraft to control the Moose.
When Deon is shot from close distance, there is a noticeable delay between Hippo shooting and the bullet hitting Deon. It seems this effect was triggered manually and not automatically via sound detection. Also lots of smoke from cheap bullet hit pyrotechnics can be seen, as well as a bulge on Deons shirt made by the blood-pack.