Christina crosses the street as traffic is stopped at a green light.
Months after the operation, after sleeping with Cristina, Paul still has a "hospital shave" on his chest.
When the doctor is listening to Paul's heart, he has his stethoscope in backwards. The ear pieces are supposed to face forward, but his are obviously facing backwards. In that position, not only would they hurt his ears, they would also hinder his ability to listen to the heart.
At the end of the movie Sean Penn states that 21 grams is equal to the weight of a stack of five nickels. Nickels actually weigh exactly five grams each so a stack of five would weigh 25 grams, not 21.
(Around the 17min mark) A top-loading washing machine would not operate with the lid open. At most, it would only fill, and not wash or spin.
When Cristina Peck wants to give blood to help Paul Rivers, a nurse uses a blood collection system called Vacutainer to collect her blood. This system uses the power of vacuum to collect blood. To do this a vein has to be pricked with the needle and then a tube must be pricked too with the other side of the needle then the vacuum does the rest. In the film we see that the tube is already pricked to the needle, so it wouldn't work.
When Paul goes in for his heart transplant, a close-up shows a needle being used to give him an injection into an IV port. The IV port shown is a "needle-less" type and does not work with needled syringes.
When Jack falls onto the ground clutching his head after Paul has fired off several shots into the dirt, you can briefly see an ear plug in Jack's ear.
When the Private Investigator gives Paul the revolver, he flips it open to show that it is loaded. He then spins the cylinder and we hear a ratcheting sound. When a revolver is open, there is no ratchet mechanism connected to the cylinder...it rotates freely and silently.
On one occasion when in Church, there is a close view of Jack, standing for a hymn. The audio is congregational singing. Jack is not singing, but the black guy to his right is singing enthusiastically, but not anything like what the rest of the church is singing.
When Cristina is getting her car and tells the valet, "I don't need a fuckin' taxi," her lips do not move.
When Paul Rivers walks away after telling Jack Jordan to leave, the cameraman's shadow can be seen on the ground and bushes in front of him.