Revealing mistake: The team going to mine the bridge waits until after dark. But as they move downstream you can see sunlight glinting off the water. Also in shots up towards the bridge you can see a lovely blue sky.
Other mistake: In the scene in the office with Jack Hawkins and William Holden, where William Holden is arm twisted into going back to the bridge, the oscillating fan, which is on and oscillating, has no blades, plus there is no breeze in the office. You can see the complete motor, plus the drive spindle, where the fan blade should be attached. It dominates the scene, along with the two actors.
Factual error: In the headquarter scenes, the Jeep's windshield wipers had a distinctive aftermarket electric motor, which was not available until after the war.
Other mistake: Near the end of the film, the demolition team plants the explosives at the base of the bridge supports, under the water. Yet, when Colonel Nicholson falls on the detonator, there are explosions on the bridge itself, far above where the charges were placed, regardless of the water level.