While transporting the Ursa all passengers on the ship are required to wear life suits in case of an emergency but Cypher doesn't take one for himself. While it is established that the character is fearless, just because you are fearless doesn't mean you can't be prepared for emergencies.
When Kitai is followed by the baboon, his dad warns him about a creature approaching him. With his advanced technology he should have been able to see the whole group and warn his son about the even greater danger.
Right before Kitai reaches the river, his father's cutlass is on his backpack. The cutlass disappears in the next shot, right before he starts building his raft, until Kitai picks up a new one at the crash site.
After Kitai climbs/digs out of the pig hole,he finds he is being followed by the mother bird and is often seen holding his cutlass protectively and yelling at her to "Leave me alone!" In the following scene he takes his final breathing fluid, but there is also no sign of his cutlass. He builds a raft,floats down stream but his cutlass is forever lost after that & we never learn how he lost it.
Before the crash, Cypher Raige straps himself into the chair with the X harness. In the next shot, he's in the background with no straps on. In the next shot after that, you can see he's strapped in again.
When the asteroids get ejected from the wormhole along with the ship, they immediately begin to slow down. In space, however, they would continue in their speed until e.g. hitting an obstacle or entering the gravitational pull of a planet.
During the voice-over at the very beginning, Cypher Raige's ability to not be detected by the Ursa is described. It is stated that "This phenomena is known as ghosting". The correct singular form of the word is phenomenon.
The first night on Earth where Kitai is hiding under a log over a thermal hot spot, it is raining heavily. However, if the temperatures plummet so that the entire planet is frozen over every night, it should have been a heavy snowfall as opposed to a heavy rainfall.