Ethan frequently uses a silencer on his Glock 17. In order to use a silencer, the barrel needs to have threads to screw the silencer to; which makes the barrel longer. In scenes where the silencer is being attached and used, a longer barrel is clearly visible. In scenes where the silencer is not used, the barrel is the standard length.
When Jules' daughter gave birth and Jules is carrying the child, you can see his daughter still having pregnancy bump in the background. Correction: As an obstetrician, immediately after a vaginal delivery the uterus remains an abdominal organ and distends the abdomen to about a 20-week pregnancy.
The hotel and the fortress in Belgrade from the beginning of the movie are on different sides of the river. It would have taken Ethan and the Albino close to an hour on foot to get from one place to the other.
Elevators do not just drop when a cable connection is either lost or otherwise interrupted by shooting; the safety system invented by Elisha Graves Otis in 1852 locks the car in place and prevents it from falling.
Ethan is diagnosed with a glioblastoma, a type of brain cancer, which in the plot has spread to his lungs. This is medically incorrect. Glioblastomas are aggressive and spread to other parts of the brain, but they don't metastasize outside of the brain.
Before Vivi gives Ethan the Glock 17, she places the slide in the locked-back position using the rear grip to pull back the slide; i.e., she did not manually place the locking pin in the locking grove. Locking the slide using this method can only be done if any empty magazine tube has been inserted in gun. Essentially, Vivi gave Ethan an unloaded gun.