What is one character trait that Romeo, Juliet, Friar Laurence and the Nurse all share that leads to Romeo and Juliet's death/downfall?
If I had to choose one trait that Romeo, Juliet, Friar Lawrence, and the Nurse all share that leads to the death of the sweethearts in Shakespeare's Romeo and Juliet, I would have to say it is their inability to view the world in a more realistic fashion.
All of these people have something vested in the love shared between Romeo and Juliet. Romeo is not realistic, nor is Juliet, with the idea that they might defy the long-standing feud between their families with any success. Hate runs high, and even the strongest love, which might break down barriers between the two young people, is not going to be welcomed by the others involved. We specifically see this in the character of Tybalt. He has nothing to win or lose when Romeo shows up at the Capulet party. Even Lord Capulet has no concern regarding Romeo's presence and orders Tybalt to let it go. However, Tybalt, the hot-head, refuses to do so. It is people like him that fuel this feud, and inevitably, his murder of Mercutio pushes the plot quickly to its tragic end.
Juliet is also unrealistic in that she is a woman, she has no way to stand up to her parents, and she—in essence—belongs to them to do with her as they wish. Defiance may be a normal reaction for a young person, and Juliet can be excused because Capulet had been so casual on the topic of her marriage before now. However, she is a young woman in a male-dominated society, and even her mother will not defy Capulet.
The Nurse is unrealistic as she allows this relationship to move forward. She may be sentimental because Juliet is like her dead daughter, Susan, and we know she loves Juliet like a child, but the Nurse is a servant. She has no say in the household and she cannot do anything to help Juliet fight the power of her parents. Instead of being forthright with Juliet, and/or going to her parents when Romeo starts hanging around, she acts more like Juliet's girlfriend and less like her guardian, and promotes the relationship until the marriage has taken place—and her favorite, Tybalt, is killed. It is only then that the Nurse changes her position regarding Romeo's place in Juliet's life. When Juliet believes the Nurse has turned her back on Romeo, Juliet cuts the Nurse out of her life.
The Friar's intentions are good: he wants to find a way to bury the strife between the two families and believes their love is the key to this hope. However, he should know enough of the sins of people, their shortcomings, and their inability to put anger behind them to ever believe the Capulets and Montagues would end their strife for any reason—short of death. This feud has been going on so long, that no one seems to remember exactly what started it. The families have been threatened by the Prince with death. If this will not stop them, the Friar should have been more realistic: for if the families would not reconcile in the face of the secret marriage, what did he expect would happen to Romeo and Juliet, even had Romeo not been banished? Would both be rejected by parents who hated their in-laws? And how would Rome and Juliet survive?
I believe all of these characters were unrealistic, and their failure to live with the realization that hearts do not change so easily leads Romeo and Juliet to disaster. (Of course, Shakespeare also told us in the Prologue that the lovers were star-crossed.)