Don't Forget the Diver - S4-E2
Factual error: While Capt. Square is looking through his binoculars at what he thinks is Mainwaring's platoon marching with their rifles, a 1960's Bedford lorry drives past on the road behind them.
Battle of the Giants! - S4-E14
Factual error: When Mainwaring is driving the van and Jones is in the back suffering from malaria, just after Pike shouts out that Jones has changed colour, if you look out the side window you can see a triangular road sign. These did not come into use until the 1960s.
Battle of the Giants! - S4-E14
Visible crew/equipment: When Hodges tells Mainwaring to pull over when he is driving Jones' van you can see crew members reflected in the left hand side of the van's windscreen.
Factual error: In several scenes during the cricket match while the Walmington platoon are bowling/fielding, cars can be seen on the road behind the cricket ground that were made well after the 1940s.
Battle of the Giants! - S4-E14
Revealing mistake: Just before the two vans drive round in circles, when Mainwaring has trouble with the gearbox, the shot from inside the van shows a house through the driver's window. But in the exterior shots there are no buildings around, just trees.
Battle of the Giants! - S4-E14
Continuity mistake: When the Walmington platoon stop their van to open the gate to let the sheep out in attempt to hold up the Eastgate platoons van the Eastgate van drives through the gate into the field with Hodges on his motorbike following, but when the camera cuts back to the road the Eastgate van and the motorbike are on the road behind Walmington's van, the Eastgate van and the motorbike are next seen coming out of the field further up the road.
Battle of the Giants! - S4-E14
Continuity mistake: When Mainwaring and Square, driving the vans, are trying to push each others' van off the bridge, Hodges parks his motorbike at the end of the bridge behind the eastgate platoon's van. In all the following shots Hodges' motor bike has disappeared.
Battle of the Giants! - S4-E14
Other mistake: Mainwaring hangs his new cap on a hook on the inside of his office door, the rest of the platoon are having bayonet practice in the hall. Pike is running with the bayonet but misses the dummy and his bayonet goes through the office door and Mainwaring's cap. The bayonet only goes through the cap once, but there are two tears in the cap.
Answer: The show is a comedy, this was played for comedic effect and to show that in times of extreme fear, in this case about to be crushed by a steam train, the men had an adrenaline surge strong enough to pedal fast enough.