Factual error: None of the German tanks are accurate representations of German WWII types. They are all post war US variants. ie. M47 Patton Tanks. [Still a mistake, but an elaboration: This is a common problem in depicting German tanks: few, if any, survived the war. The few museum examples wouldn't be released for movie work, and certainly WHERE, some 20 years after the war, would one find a brigade's worth of running Tiger II tanks? Never mind that Kampgruppe Pieper, which Hessler's command is loosely based on, actually used Mark IV and Panther tanks. There was one King Tiger battalion, and it was in reserve well behind KG Peiper. The M47s versus the M24 Chafees (mistakenly called "Shermans" at times) is a fairly accurate comparison of the respective sizes, firepower, and other combat capabilities of the respective tanks. Some other movies, like "Kelly's Heroes", have their "Tigers" mocked-up with sheet metal, wire mesh, and sacking over a different type of tank (in that case, T-34/85s of the Yugoslav army are mocked up as Tiger Is, a fairly decent job).]
Continuity mistake: Near the beginning, Lt. Col. Daniel Kiley is in a scout plane and flies over Col. Martin Hessler, who is in a German staff car below. Kiley tells the pilot to "rev the engine" just above the car to entice Hessler to look up at them, so he can get a good photograph of his face. The plan works, and the ground level movie camera shows Hessler looking up. When the "photo from the air" is later developed, it shows Hessler looking up from the ground level camera's perspective, eyes focused about 30 degrees behind the airplane and giving a profile of Hessler.
Factual error: All of the jeeps used by American forces are of post-war design - most probably CJ-3 (M38) models - recognisable by their one-piece windscreens. Some of them have been modified to somewhat resemble the WW2 model by moving the spare wheel to the rear, but most of them still have the spare fitted to the side further identifying them as post-war models.
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Factual error: During the scene (near the end of the film) in which Col. Hessler's tanks attack a hilltop fuel depot, American GI's counterattack by rolling burning 55 gallon gasoline drums at the German tanks. When one of the burning drums hit Col. Hessler's tank, the tank IMMEDIATELY explodes and its turret blows off. The blowing off of the turret indicates that something inside the tank (most likely the ammunition) exploded. However, in order for a burning gasoline drum to cause such an explosion, the burning gasoline has to heat the interior of the tank to make it hot enough for the ammunition inside to explode.
Deliberate mistake: In the scene inside General Kohler's command center when Kohler is giving Colonel Hessler a tour of the war room he points out to Hessler a clock on the wall whose increments represent 1 hour and that the attack has to be over within so many hours. Later in the movie, just when the attack starts, this dormant clock's hand immediately springs forward and ticks through 2 increments, thus representing 2 hours passing in 2 seconds.
Factual error: The German panzergrenadiers follow the tanks on foot right from the beginning of the advance. Panzergrenadiers were armoured infantry and travelled in halftracks, only dismounting to fight. Even ordinary infantry advancing with tanks would have used trucks - to do otherwise would have slowed the tanks down to a crawl and rendered them ineffective. There was a shortage of fuel in the Ardennes campaign, but the panzergrenadiers did use vehicles during the advance (except for a couple of battalions which used bicycles).
Factual error: At German Army headquarters, the General tells Hessler of the new Tiger tanks that will be used in the offensive, which takes place mid-December 1944. Presumably, these are the Tiger II (King or Royal Tiger) models. At this point in the war, "King" Tigers were not new, having fought against the British and Canadians in Normandy back in July of 1944, and against the Americans at Aachen in September of 1944.
Continuity mistake: In the initial German panzer attack against the Americans, a German tank 104's left side track and road wheels are damaged by a bazooka shell, resulting in a missing front road wheel and a loose/sagging track. However, when the tank turns off the road and goes down the slope, the left track is taut and the missing road wheel has magically appeared.