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This seems awfully vague for a post claiming that somebody did the math wrong. If you believe it's wrong, why don't you run through exactly what the wrong calculation is, why it's wrong, and how to do that calculation correctly? I suspect whatever you're alleging will fall apart when you do that.
As a simple issue, yes of course the actual Earth is not flat, and the entire surface is not bathed in sunlight 24/7. These seem likely to be simplifying assumptions to me. If you wanted to calculate the amount of energy that the Earth received from the Sun, then it would in fact be a very reasonable idea to model the Earth as a flat disc constantly facing the sun. The amount of energy that the Earth actually receives from the Sun should match this model pretty well, since it accounts for the actual effective area facing the sun on our roughly spherical and rotating Earth. Your objections aren't novel, you just haven't noticed or accounted for the fact that they're intended to cancel out.
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