Goofs

Godfrey is wearing a slipper on his left foot for the entire episode except when he gets in the back of Jones' van wearing two shoes.

After Mainwaring is taken up by the balloon it is reported to the RAF as an unidentifiable object where the officer in charge says to "scramble 7 squadron". At this time 7 Squadron were flying Stirlings (the first to have this 4-engined heavy bomber) and would be way down on the list of squadrons that you would want to solve this particular problem.

As Mainwaring is dangling from the railway overpass and the platoon is trying to rescue him, the train passes beneath, engulfing everyone in smoke and steam. However, there are also flames visible. A coal fired steam engine will eject embers through the stack, but any flames would be extinguished by steam exhausted through the smokebox into the stack.

The verger descends into shot supposedly clinging on to a rope attached to the barrage balloon, but the wire which was really supporting him is visible.

Helvetica font is seen in use at the command center. This font was created at least 12 years after the time of the action.

At 22 minutes 50 seconds the hand of a crew member can be seen in the bottom left of the picture presumably to make him move around on screen while he's holding onto the rope from the barrage balloon.

During the short scene in the RAF Operations Room where the UFO is identified as Barrage Balloon Amy.