Judging by Choltitz's own memoirs ('Soldat enter Soldaten", 1951) there never was an order to deliberately destroy Paris or its monuments. The orders concerned laming industrial plants, blowing bridges, crushing uprisings, and defending the town as a fortress, accepting collateral damage. Choltitz later found out these orders were addressed to his superiors, not to him. He does mention Hitler asking "Is Paris burning?" but says he was informed of this by others, whose names he does not give.
German sappers are shown setting conventional explosives on Paris bridges. The Germans actually set used surplus naval torpedoes under the bridges.
At the end of the movie, the lieutenant Henri Karcher calls his father to tell him he has just captured a general. Actually, his father died in 1914.
Some of men's suits, both male and female haircuts and male spectacles are clearly from 1966.
At 1:03:15 in the scene when the German vehicle hits the tree, the soldier in the passenger front seat seems to have the wherewithal to stand up after hitting his head on the gun propped against the dashboard, he stands up in a staggering way, firmly grasps the barrel of the gun and pushes it aside just before he 'dies' on the hood of the vehicle. It is as if the actor clearly didn't want to "die" in an uncomfortable position.