In the final scene, Chakotay and Janeway talk outside the holodeck. Chakotay's hand-wraps are white. When the scene shifts to the holodeck, his wraps are yellow.
In Sick Bay when the Doctor explains to Janeway and Chakotay how the brain of the captain from the derelict vessel has been changed, Chakotay declares that he must go on a vision quest. After the Doctor gives Chakotay permission and a cortical monitor, the scene moves to Chakotay's quarters, where he is seated on the floor, and we see the familiar elements of him beginning a vision quest. After having the experience for a while, Chakotay suddenly returns to regular consciousness - but he's sitting up from a bed in Sick Bay.
When Chakotay gets punched in the boxing ring, he falls face first. When the camera changes, he's landing on his back.
Chakotay spends much of the episode with his hair somewhat sloppily combed forward, which makes sense since he is often sweating from boxing or from the mental discomfort caused by the aliens speaking in his brain. The hair goes from forward to combed back throughout, but this is largely because the timeline shifts between the present--when Chakotay recalls events to the Doctor--and the events themselves.
However at one point the hairstyle changes for no reason. At 11 minutes Chakotay has had a chance to comb his hair back before he enters the bridge but it is over his forehead again after the hallucination episode on the bridge lands him in the infirmary. It's then combed back again right as he starts and finishes his vision quest, but forward when he's once again in the infirmary. It is likely that the infirmary scenes were all shot at the same time, and the set managers mistakenly had the hair style the same way in every scene.
However at one point the hairstyle changes for no reason. At 11 minutes Chakotay has had a chance to comb his hair back before he enters the bridge but it is over his forehead again after the hallucination episode on the bridge lands him in the infirmary. It's then combed back again right as he starts and finishes his vision quest, but forward when he's once again in the infirmary. It is likely that the infirmary scenes were all shot at the same time, and the set managers mistakenly had the hair style the same way in every scene.
When Chakotay gets punched in the boxing ring and lands on the mat his tattoo doesn't have a cut on it. The next scene when he's in sick bay you see a cut on his tattoo.
When Chakotay gets hurt in the boxing simulation he is shown to have no cut on his forehead after he lands on the mat. However, when he goes to Sick Bay he is shown to have a cut on his forehead. Clearly a mistake.
When the Doctor says he is going to sing at 880 Hz (A above high C), he in fact sings at 440 Hz (A above middle C).
Towards the end, Tom Paris addresses Captain Janeway as "sir," which she has expressly discouraged her crew from doing since her captaincy of Voyager began. The exact same thing happened in the previous installment Course: Oblivion (1999).
The Doctor is a self-aware hologram. He cannot "die" as such and is aware of that (e.g. the vacuum of space cannot kill him). His program can be de-compiled, but that is neither "death" as such nor the actual fate that is awaiting him and the other crew members (they will die of exposure - which won't affect him). Yet he tells Chakotay "we will all die here" if Chakotay doesn't allow the aliens to help.