Revealing mistake: During the car chase scene, if you watch the speedometer on the car, it never rises above zero. That, and the obviously poor image quality of the "road" in front of them, shows that they were using projected film in front of the car.
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: 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.
Revealing mistake: In the scenes inside the space capsule, as Roy goes through the sequence, the wires holding him up in the floating sequences, and the crackers when trying to eat, are visible.