As observed by the previous answer, the messengers' flaws contribute to the narrative, bringing out thematic contrasts between characters and/or creating dramatic issues.

The incident between Juliet and her Nurse emphasizes how the Nurse is out of breath and taking forever to get to the point of her message. The young, impatient Juliet laments that the Nurse is torturing her by taking much too long to say what she needs to hear. This creates a contrast between age and youth, which is one of the themes of the play. In a comic way, it also prefigures the widening gulf between Juliet and her Nurse, a previously maternal relationship which ultimately breaks when the Nurse tells Juliet to betray Romeo after his banishment from Verona.

Balthasar's error also relates to the themes of age and youth. Young people in Romeo and Juliet are often portrayed as rash, and Balthasar's error of assuming Juliet was dead without knowing the whole story (not even checking out how she allegedly died or telling Romeo to wait for further information from Friar Lawrence) is a continuation of that thread.

Friar John was dedicated to his task and his inability to deliver the message did not come from a character flaw, as with the Nurse or Balthasar, but from external events beyond his control. He was quarantined, unable to continue delivering the message to Romeo in Mantua. This intervention of outside forces also reflects how Romeo and Juliet's love is opposed by outside forces-- their families, their society, fate itself. In the end, outside forces appear to push them to their early graves.