Your question is quite large in potential scope, so I will focus on the use of comic relief in the play. Shakespeare actually used comedy quite a bit (and quite effectively) in his tragedies. If you think about it, there's quite a bit of tension that develops when an audience is on pins and needles waiting to see what will unfold as the drama builds. Shakespeare understood this and often inserted comic moments (even in highly dramatic scenes) to help relieve the tension for the audience. So, in this answer, I'll be using the terms joy and sorrow to relate to the audience's experience of the events rather than the characters'.
Two major characters in Romeo and Juliet that can be noted as central to the dramatic plot, but also providers of comic relief, are the Friar and the Nurse. And both provide comic relief for the audience in highly sorrowful/tragic moments.
Once the Nurse discovers Juliet's cold, seemingly dead body and calls the Capulets in to see their daughter, Shakespeare gives her some rather awkward lines:
O woe! O woeful, woeful, woeful day.
Most lamentable day. Most woeful day
That ever, ever I did yet behold.
O day, O day, O day, O hateful day.
...O day, O day, O woeful day.
Compared to the speeches of Lord and Lady Capulet that speak eloquently of their love for Juliet, this text seems to be more an echo of Bottom's silly send-up of Tragedy as Pyramus in the mechanicals play in A Midsummer Night's Dream.
However, what if Shakespeare was using the Nurse to show how sometimes in the most tragic circumstances, people behave in humorous ways? If the actor playing the Nurse puts everything they have into these lines, it seems that the audience will potentially find it funny. And at that moment, Shakespeare has shown, in his genius, the comic in the tragic.
A smaller, but equally telling use of a comic moment smack dab in the middle of a tragic event is at the end of the play when the Friar is hurrying to get to Juliet's tomb ahead of Romeo. The Friar's text:
Saint Francis be my speed. How oft tonight
Have my old feet stumbled at graves. Who's there?
This text indicates some very old and basic comic devices: one -- that he stumbles (a character tripping onstage is always funny) and two that he is immediately jumpy, wondering what bogey man is there in the darkness of the tomb. The moment is creepy and tense for the audience, and it seems just right, dramatically, for Shakespeare to have intended this small moment with the Friar to provide some comic relief.
Just a possible answer, but the best i can think of is right at the beginning after the first fight we see between the Montegues and Capulets when Romeo tells Benolio "Here's much to do with hate, but more with love" and has his speech. Or perhaps when Juliet says "My olny love sprung from my only hate, too early seen unknown and known too late. Prodigious birth of love it is to me that I must love a loathed enemy". Those are the best two ican think of.