When a Burmese woman spreads a masking paint on Major Shears' legs, before they are to set charges onto the bridge, it's clearly seen that William Holden is wearing 50's style loafers, that not only do not fit the time, but don't fit the situation at all.
Japan was not a signatory of the Geneva Conventions until 1953, therefore there was no expectation by Allied prisoners of being treated in accordance with them. In fact, the Japanese treatment of prisoners led to the review and update of the conventions in 1949.
Saito tells Nicholson that he spent three years studying at London Polytechnic, which would presumably mean he would learn the British pronunciation of English words. But while he does refer to his own officer, Lt. Miura, as "Lef-tenant", he also complains that the bridge will not be completed on "schedule", using the American pronunciation, with an "sk" sound, instead of the British "sh" sound his education and experience in England should have led him to use.
When Col. Saito leaves Col. Nicholson and the other officers standing in the sun their shadows lengthen during the day. The scene then cuts to a view from inside the 'hospital' and the shadows of the officers are noticeably shorter.
As Major Shears and the others are parachuting, the POV is the audience looking up at them coming down. There are some white clouds, and a lot of clear sky. Cut to their guide waiting on the ground, watching the men for a few seconds. Cut back to the audience POV looking up, and the sky is now all dark clouds.
The end of the opening sequence shows a railroad car with a machine gun approaching the end of the railroad. There are perhaps a dozen workers milling around in front of the car. A subsequent longer shot shows many more workers and a longer length of track in front of the car.
During the first two formations in front of Col Saito's office, the sun is behind the men, yet we can see some shadows in their foreground, caused by the movie lights behind or to the sides of the cameras.
In the opening scene, the railway is 5'6" (1.676 m) broad gauge, as used in Ceylon (Sri Lanka), the filming location; but when we see tracks on the finished bridge, they're much narrower, about 2' (60 cm).
Many Japanese POW camp commandants equipped their guards with British equipment because of an abundance of British ordnance after the fall of Singapore in 1942 and the difficulties in equipping main line troops with new equipment so far from Japan, much less camp guards who would not be near the fighting and would not require constant resupply. The warring nations equipped prison camp guards with second hand equipment. As such, it is not a goof that the Japanese soldiers do not have Japanese weapons.
It wouldn't have been necessary for Joyce, the Canadian, to go to the UK to enlist to fight against the Japanese, as he says when being interviewed to join the commando group going back to the Kwai. Canada joined the war only ten days after war was declared by the British, and Joyce could easily have enlisted at home in Montreal. However, Joyce may have wished to serve in an elite commando unit such as the SAS, which Canada lacked, or to serve in the Pacific, which, due to Prime Minister William Lyon Mackenzie King's 'limited liability' policies, Canada's involvement in the Pacific was limited to the Battle of Hong Kong in 1941 and the Aluetian Islands in 1942.
While the prisoners are all supposed to be sick and/or mistreated, in fact all look reasonably healthy and even tanned, and none in any kind of starved or emaciated state. In reality, as numerous photographs of actual prisoners of the Japanese show, all prisoners were uniformly emaciated, having lost an enormous amount of weight, starved, and with skeletal frames - conditions noticeably absent from any of the prisoners in the film. However, Saito was based on one of the more humane commandants who was acquitted of war crimes after war's end.
At the start of the movie, while the officer's and men are marching, they whistle. Unfortunately, while their whistling is meant to help keep them all in step, the music does not match their marching steps. In fact, had they been marching in step, their left foot would have been on the first and third beats of the song. This is done intentionally to show that at the beginning, the soldiers are disorganised and unable to whistle and march to the beat. When the theme plays again at the end, after the bridge has been built, they all whistle and march perfectly, showing their progress.
Although the explosives were planted at the bases of the bridge piers, when the bridge is blown up, multiple explosions are also seen at track level, far above and away from where the explosives were actually planted.
The goof items below may give away important plot points.
During the bridge completion celebration Nicholson gives a speech on the stage while Shears and Joyce are placing the explosive charges under cover of darkness. In some shots, the camp is visible in broad daylight beyond the left edge of the stage backdrop behind Nicholson.
The morning of the explosion, the sun rises upstream of the bridge. When Nicholson finds the exposed wire snagged on the sunken tree, he is squinting into the sun, upstream. All the rest of the action, including the snagged wire, occurs downstream.
When Nicholson falls on the dynamite plunger, the charges on the bridge are set off several seconds apart. Being on a single wire, with a single plunger, both charges should have gone off at the same time. Two separate charges would require two separate plungers (and two separate wires).
Towards the end of the movie before the bridge is blown up, the soldiers are seen marching across the bridge on their way to a new camp. From the long shot it is not clear that they are marching in step, but it is clear from the sound effects. It has been a widely used practice since 1850 that soldiers marching across bridges will break step so as not to cause any undue resonant stress on the bridge and may cause it to collapse. While this notion that a bridge will collapse is still under debate, it may be that the scene shot in the film proves the exception.