(at around 27 mins) When Claire and Eric are painting together in his apartment, Claire's brush strokes are missing when we see the painting again.
(at around 38 mins) When Arkin comes to visit Claire at her group therapy room there's a cut of Arkin talking with the first person that approach him. Then we see a cut of that person talking with Arkin. Followed by a cut back to Arkin responding to that persons answer. During the first cut of Arkin we clearly can see someone in the background walking downstairs. That person walks down the same steps when we see the second cut of Arkin talking.
(at around 27 mins) The painting in the scene when Claire and Eric are in his apartment changes from when Eric first gives Claire the brush to when she first begins to apply paint. It is mainly blue but suddenly has all this white at the bottom and the shape of the blue is very different. Then it changes again when they show them from the left, and then again when they step back from it.
(at around 57 mins) After Claire leaves Norman's apartment one of the passengers tries to keep her from driving away. The first screen shot from inside the car shows her pulling away. The camera angle then cuts immediately to a shot from outside the vehicle and shows the car stationary for a split second just before Claire pulls away. The editing is off by about a second.
(at around 46 mins) When Claire jumps from the boat to save Eric, she's wearing her PFD (orange life vest). When seen in the water with Eric, she's clearly not wearing it. However, when she puts the life vest on, she does not tie or fasten it correctly, and, when she jumps in to the water, the vest can clearly be seen coming off, and bobbing around in the background.
(at around 1h 16 mins) When Claire is going through the pilot's logbook on the porch, you can see that most of the blocks on the right-hand page have "check marks" in them. These blocks should have "hours" in them for conditions of flight - how many hours were at night, in instrument conditions, etc.
In the Special Thanks credits for the "Making of" featurette on the DVD, Andre Braugher's first name is misspelled Andrea.
(at around 37 mins) When Eric visits Claire at night at her apartment, you can see food and water bowls for a dog/cat by the door, yet there is no sign of a pet at anytime in the movie. The bowls disappear at the end of the movie when Emma visits.
(at around 3 mins) When Perry encourages Claire to counsel the survivors of the crash, he explains that she has 2 MSc and a PhD that never ends (so she has still not completed it). However later on (at around 22 mins) when she gives Norman a lift in the car, he repeatedly calls her "Doctor". She has not yet completed her PhD - so she is not technically Dr Summers, as a counselor or psychologist is not the same as a psychiatrist. We know that Claire is not a psychiatrist as she tells Shannon in the focus group that she can ask if a physician will prescribe something to help her sleep. If Claire were a psychiatrist she could prescribe the pills herself.