What is the key flaw of Odysseus in The Odyssey by Homer?
The Odyssey by Homer is not a tragedy, and thus one cannot expect to find a traditional "tragic flaw" in the character of Odysseus. That being said, Odysseus is a somewhat unconventional hero.
On a basic level, Odysseus has many of the standard characteristics of the hero of oral epos. He is the ruler of Ithaca, descended from a noble family, with some elements of divine ancestry. He has a powerful goddess, Athena, the goddess of wisdom, as his patron. He is also unusually strong (as suggested by other people's inability to use his bow) and a skilled warrior.
On the other hand, unlike the typical hero, he is clever and sneaky, often preferring underhanded stratagems to straightforward honorable battles. He is sometimes too proud of his own cleverness and too inclined to boast at the wrong time. He would have successfully defeated Polyphemus and gotten away with it had he not taunted the Cyclops after escaping and told him his real name. Thus we can conclude that pride in his own cleverness is his key flaw.