Watch out for these mistakes when proving greedy correctness:
Assuming greedy is optimal without proof: : "It seems like it should work" is not a proof.
Proving greedy is good, not optimal: : Showing greedy gives a valid solution is not enough. You must show it is as good as any other.
Incomplete exchange: : Forgetting to show the swap maintains validity (not just quality).
Wrong measure for stays ahead: : The measure must be comparable at every step.