Helen and Paris fell in love causing a problem because she is already married to Menelaus. The greeks may have taken from this are that its bad to steal each other's girlfriends.
Agamemnon attacked troy for his brother Menelaus. The greeks could have learned from this that family comes first.
Patrocles and Hector had a fight which ended in Hector killing Patrocles. The Greeks could have learned from this that the cities hero will stop at nothing to protect them.
Achilles is a demigod who when he was a baby his mother dipped him in the river by his heels making weapons being unable to harm him. The greeks may have taken from this that motherly love with does anything to protect their children.
Achilles fights Hector because he is outraged with Patrocles dying and kills Hector. The greeks might take from this that anger can make people do some wild things.
These events lead up to the creation of the Trojan war. The greeks could have learned from this that a small problem could cause a major war.