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Even with all the factors listed above, I'd be disappointed too if the last shot is representative of the performance you're getting from your 1D3.
70-200/2.8L Mk II on a 1D Mark III, outdoors, sunny day, high contrast uniform, ISO 100, shutter speed 1/1250", AI Servo... all sound like ideal picture taking conditions.
Focus point on the eye, I'd expect it to be razor sharp even when pixel peeping at 100%. Soft and looks like a lot of CA, too. Like you're using a cheap TC, but you're not. Especially since you know the 70-200 Mk II is tack sharp on other bodies... the AF on your 1D3 should definitely outperform your Rebel.
I'd definitely do a micro focus adjustment on it.