According to Olivia Hussey, the camera used for filming, Arriflex, was very loud. As a result, the dialog had to be looped, and recorded separately later.
When Romeo runs to find Tybalt after Mercutio dies, Balthazar runs after him and loses his hat in the square. But when he catches up with Romeo, his hat is back on.
In the opening fight between the Capulets and the Montagues, Tybalt gives Benvolio a very nasty stab to the eye (area) with his sword. Then, in the next scene, when Benvolio meets Romeo, he shows absolutely no sign of any injury or distress.