Shakespeare's point? Infatuation makes people stupid. Romeo is a courtly lover--he takes sick, hopes for pity, and spends his hours pining for a woman who has rejected his every move towards her when the play opens. He continues to act impulsively and extremely as the play progresses. Even Juliet, arguably the most level-headed of the two, acts impulsively. She tells him she loves him (albeit unknowingly) before she's even had a second date, and then she offers to stand on form afterward--if he thinks he needs that.
Their deaths could have been avoided with a little patience and careful prodding, that's for certain. The issues around the ancient feud are also important, for the feud plays as great a part in the outcome as does the character of the two lovers. The commonality between the feuders and the lovers is that both act on intense, extreme emotion, are given to impulse, and create the ground that allows them all to become fortune's fool.
While it is true that Shakespeare took his idea for this and many of his plays from other works, the most obvious "lesson" here is don't sweat the small stuff. No one from either family remembered what the original feud was about, so why continue hating one another? This is true for so many family feuds over the centuries. The fact that Shakespeare has the only children of both these families die for forbidden love of one another is a poignant ending to a bitter hatred.
Shakespeare took the plot of the play from a drama written by Arthur Brooke in 1562 and republished in 1587 as The Tragically Historye of Romeus and Juliet. It was an Italian poet who first wrote the story of doomed lovers in 1530. Feuds between families that were obstacles to true love dates back to ancient Roman and Greek comedies.
Shakespeare took this idea and certainly made it his own. He was the first to dramatize the story and reduced the time period of the action of the play to just a few days. I think it is ingenious that Shakespeare tells us from the beginning that Romeo and Juliet will die. For me, this served to increase my desire to read the play and see it performed.