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 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.
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.
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.
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.
The poster for the movie states that 21 grams is the weight of a stack of nickles, a chocolate bar, or a hummingbird. A U.S. nickle is 2.5 grams, the same weight of a hummingbird, so 21 grams would be about 8.4 of either (which would be impossible unless you cut one nickel in half). A standard Hershey's chocolate bar is 43 grams, and many other brands weigh even more, making 21 grams less than half of a chocolate bar.