School boys are shown firing a .303 Vickers machine gun, which had a range of 4,500 yards. An outdoor firing range would always have a slope of earth or sand behind the targets to stop dead all bullets fired down the range. Not only is there no such slope behind the boys targets, but we can see they're firing down into a valley full of buildings, well within the 4.5km (2.8mi) range of the gun, jeopardizing the lives of the villagers!
In the opening shot of the scene where the schoolboys are practicing firing their machine gun, a large white modern articulated lorry can be seen moving from right to left in the background behind the targets.
Tubular metal scaffolding (of the kind that the Doctor dislodges with a thrown cricket ball in order to save the woman and child from a falling piano) was not in widespread use in the UK until the 1930s. Before that, wooden scaffolding poles were employed, lashed together/into position with rope or something similar.
Given the importance of the watch, it makes no sense for The Doctor to keep the clock himself instead of giving it to Martha to make sure she can carry out her task at a moment's notice if necessary.
Just after Joan, Martha and Jenny see the flare in the sky, John Smith tells them it's just "a meteorite." However, the correct term is meteor; meteorite is used for once it has landed on the ground - as in a rock that originated from space that fell to earth.