Continuity: In the scene where Edward and Carter are on the plane, Edwards book keeps changing position from mostly open to mostly closed, as well as the amount read varies.
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Mistakes
When Cole and Carter are skydiving, there are a number of inaccuracies. First, Carter and his instructor jump well before Cole to put a safe distance between them. However, Cole and his instructor immediately catch up to Carter and then match their speed. This could be achieved by skilled jumpers, but not by instructor-novice pairs. Second, the men have a conversation while free-falling, which is completely impossible. Third, Carter pulls his own rip-cord (too early) and Cole's instructor yells at him to pull his own cord before it's too late. In reality, the instructor always carries the chute and pulls the cord for a first-time jumper, for exactly these reasons. See more...
The Bucket List mistakes
Continuity: While racing, Carter crashes against a wooden barrier, splaterring its bits all over the race track. When the angle changes the road is clean.
Continuity: In one of the scenes in the hospital room, Morgan Freeman puts on his glasses. The next camera shot shows him with them off, then on again in the next shot.