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.
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
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.
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.