The crossbowmen had kind of already lost the arrow-fight, but anyway that's the limitations of the feudal chain of command and period methods of communication (ie. shouting loudly) for you. C^2 issues were actually the main reason the French armied seemingly paradoxically tended to perform way better when they were small, and blundered disastrously when they were large.
As far as military mistakes go... if Operation Barbarossa was heavy on the desperate gambling, wistful thinking and pure blinkered superiority complex on the part of the Germans, their initial success was most certainly greatly assisted by the blunt fact that when it came to the disposition, deployement etc. of the Red Army in Poland Stalin had picked up the Idiot Ball and hung on to it quite stubbornly. Massing the divisions densely right at the border just meant the German assault promptly overran through both lines before the reserves had any time to react, nevermind now being something of a textbook example of How Not To Deploy Your Forces Period anyway. Putting an incompetent sycophant in charge of the whole front for the better part of the peace period, and then pretty much panicking and issuing idiotic orders to the commanders when the Germans attacked, weren't exactly Uncle Joe's brighter moments either.
End result was that the Soviets had to fight a desperate rearguard action all the way to the gates of Moscow with shattered remnants and hastily raised conscripts until the massively overstretched German logistics finally keeled over...
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