Visible crew/equipment: As Quatermass drives back to the spaceship in a cab, just before it is to be drilled, the film crew can be easily seen in the cab's windows. A woman with a white cap can be seen holding a script. Later when the police use a megaphone on their car to announce the spaceship is a hoax, you can again see the same woman with a white cap in one of the windows of the police car.
Suggested correction: How could you tell if the reflection showed the actual film crew and not just a TV and newsreel crew assembled for the scene? They were also using mounted cameras and carrying papers.
Continuity mistake: During the car chase, the police car overtakes the car it is chasing which then suddenly turns left. The police car brakes, then reverses and turns left to continue chasing the car. As the police car turns, there is a grey Mini parked on the right that wasn't in the previous shot and couldn't have appeared in a few seconds.
Factual error: The problem with firing a cannon on steam power is to have the boiling water build enough pressure inside the barrel, with no leaks or openings to release it before its time. The professor's scarf and the plug hammered into the fuse hole (which also flies off just before the shot) wouldn't be good enough as pressure restrainers.
Continuity mistake: At the beginning, the scientists are told they are being sent to study the strange fact that seven meteors landed near each other in a V formation. The government agent even traces a V on the board with his finger. When they get to the field, panoramic shots show that there are nine meteors, and they are in a 3 by 3 grid, not a V.