Finding flaws in Beowulf is not an easy task. As an epic hero, he stands as the archetype of the early Germanic/pagan Anglo-Saxon warrior, and he also devoutly embraces Christianity. Beowulf depends upon God's help in waging battle to defeat evil and frequently gives God the credit for his success. He is humble before God.
As for character flaws, perhaps boasting might be considered a flaw. Beowulf's confidence in himself sometimes appears to others as a kind of pride or cockiness. This is seen in Beowulf's relationship with other characters, including Ecglaf and Unferth.
Even at the end of his life, as an old king, Beowulf maintains his self-assurance: "I have never known fear, as a youth I fought / In endless battles." Beowulf continues that even though he is old, he will fight once more "If the dragon hiding in his tower dares / To face me.
I would actually have to disagree with mshurn. Beowulf is flawed because he does not boast enough. In this time period the vikings are all worried about achieving val-halla (viking heaven) and the only way to do so is to die noble in battle. To be humble and not boast would be the christian side of the story however the vikings religion is Norse in which it is expected to boast, almost always otherwise you are frowned upon. Eventually Beowulf's men do frown upon him so he goes to kill the dragon.