The model of the dam shown to Maj. Powell at the beginning of the film looks nothing like the dam that is blown up during the climax.
Many of the British commandos wear Royal Marine berets and crests. However, in WWII Royal Marine commandos were trained for amphibious raids and not as paratroops. Paratroop commandos were trained by the British Army and the unit is commanded by an army major.
The inflatable boat and some of the scuba equipment used by the commandos is too modern for WWII.
The camouflage worn by the British commandos, and the major's rank tabs, are of a post-war style not in use in 1944.
Although the Wehrmacht (army) uniforms appear accurate, the SS uniforms have oversized collar patches and Holtz's collar is too high and non-standard.
The SS NCO who stops and searches the wagon is wearing two different ranks. His collar insignia is that of a SS Unterscharfuhrer (junior squad leader), but his shoulder straps are those of a SS Oberscharfurer (senior squad leader), which is two grades higher (or the difference between a US sergeant and sergeant first class.)