Revealing mistake: Leonardo DiCaprio blinks after he dies. (01:50:28)
Continuity mistake: The nurse changes position in the church.
Visible crew/equipment: On the DVD, when the Capulets are jumping back into their blue car at the end of the gas station scene, look at the rear passenger window. A microphone boom is plainly visible in the shot. (00:07:21)
Continuity mistake: Just before Romeo and Juliet jump into the swimming pool, Juliet's hair is in a braid that wraps around her head. But, when they jump into the pool the braid is gone.
Continuity mistake: When Romeo is talking to the Capulet father at the party, his mask goes up and down.
Continuity mistake: In the gas station at the beginning, when Jamie Kennedy is singing "A pretty piece of flesh I am", watch his shirt. When he is first walking forward it is buttoned, then, in the next shot, it is open when he is licking his nipple. It's too quick a shot to have unbuttoned it.
Continuity mistake: After the prologue, you see the Montague boys in the yellow car. If you look at the Montague sitting in the back of the car, you can see that his sunglasses are on his forehead; a few seconds later he puts the glasses down over his eyes. In the next shot, his glasses are back on his forehead again.
Continuity mistake: Romeo has just come up from under water, where he was hiding from a guard. His hair is untucked and messy. In the same scene seconds later it is combed back behind his ear and smooth.
Visible crew/equipment: Just as Romeo is about to leave the courtyard after his antics in the pool with Juliet, he turns around as she calls him from the balcony to give him her necklace. As he turns quickly look above Romeo's head, the boom mic quickly pulls out of the shot.
Continuity mistake: Tybalt's tattoo changes constantly. When he's watching Mercutio dying on the beach, it's a plain simple heart on his chest. When Abra is forcing him to run away to his car (in the same scene) it is not there at all. Then when Romeo is chasing him in his car and Tybalt's car rolls over, as he crawls out, it is much more intricate, with black lines and fire. It also changes when he gets shot over the fountain.
Continuity mistake: During the scene where the Montagues enter the Capulet mansion, watch the chain linking Romeo's armour on his back. At first it is attached, and then it is broken, then later attached again.
Continuity mistake: When Romeo goes to the old man to get the poison, he opens the door and you hear the sound of a pump action shotgun. The gun he uses is a normal break action shotgun.
Continuity mistake: When Romeo and Juliet are in bed and Romeo playfully pulls the sheet up over his head, his shirt gets caught in the sheet and ends up over his shoulder and around his neck, but in the next shot from the side, his shirt is down.
Continuity mistake: Immediately before Romeo comes into Juliet's room, Juliet is looking at her religious statues, and you can see her right cheek is wet with tears. When Romeo comes in and Juliet turns around to see him, her cheek shows no signs of tears, nor after that.
Visible crew/equipment: Near the end when Romeo is having a shootout with the police at the church, look closely at the door to his right. There's a bit of wiring or something there. An officer fires a shot toward Romeo and you can then see that the wire is actually the flare/effect for a bullet hitting the door. (01:40:00)
Continuity mistake: In the balcony scene, Romeo knocks over a metal stand in his panic as the lights come on. It clatters to the floor but in the next shot it is standing up in its previous position.
Continuity mistake: In the beginning of the film, when we see the Montague boys in the car, the bald one has an uncoloured tattoo, but it's coloured yellow later in the film.
Continuity mistake: When Romeo and Juliet are lying in the bed, you see from one angle that Romeo has a little bit of a sheet lying on him. Then you see him taking the sheet off from Juliet's eye angle, but from that angle there is a lot more sheet on him than before.
Revealing mistake: When Benvolio is running away from Tybalt and the fire, there are two Policemen visible who could be doing something about the gunfire etc. My guess, not supposed to be in view. (00:07:55)
Continuity mistake: When you first see the Capulet mansion, Juliet's mother is calling her. When she sees the nurse, the nurse's hairnet is at her hairline. When she goes to find Juliet it is at her eyebrows and it goes back to it's original place when Juliet is found.
Answer: Whatever songs are in the movie were licensed for distribution by the film production company for a fixed price. It is impossible for there to be later fees somehow incurred on the production company just because the group is more popular. However, it's conceivable that Radiohead only allowed their song for use in cinemas but not television.