While being halfway through shaving (with some sort of laser razor), Bower gets interrupted by a tremor. In the next wide shot he appears to be suddenly done shaving, but he's simply finished and this is a "jump cut" to condense time.
When Payton traps the insane officer 'Eden' inside the sleep capsule Eden's arms are by his side in the shots from the outside. When we see the capsule from the inside Eden's arms are up against the glass.
Right after Bower climbs up the ladder out of the small tunnel after asking Payton about feeling symptoms of Pandorum and the Eden mission, he is holding the flashlight in his right hand, the same hand as the gauntlet, as he walks away it suddenly switches to his left hand.
They ejected from the ship with the escape pods, but decompression sickness would have killed everyone after a short time.
When Bower is attempting to awaken Payton by banging on his tube, it reads Payton from the outside. In a reverse angle from inside the tube, it clearly reads Bower, indicating the tube was reused from the earlier sequence when Bower awakened.
In the suit of one of Eden's crew members it reads Kreska, however, in his respective hibernation chamber it reads Kresca, with C.
The cargo containers where Nadia's shown to live are obviously of 21st century design and manufacture. Since the film is set nearly 200 years into the future, it's a certainty that these types would not be used.
In the bio for Antje Traue, it says she had a role in the Superman movie "Man of Steal". That should be Man of Steel.
Payton is shown wielding what is known as a Halligan's tool, a firefighting device invented in the 20th century and commonly used in modern times. 200 years into the future such a tool would have been replaced by dozens of newer devices as it is currently being supplanted now.
The ship has reached destination and been there for 800 years. How or why most of its systems are still functioning and why there's still edible food (other than the passengers) on board is never explained.
As with many space-based movies the whole issue of gravity creates a problem however, unusually, in this case it is a character error as opposed to a plot hole or a revealing mistake. It is revealed at the end of the movie that the space ship has already landed on an earth-like planet, so is is perfectly reasonable that earth-like gravity applies throughout the movie, however the fact that this gravity is present on board should have revealed to the wakening crew that they were not traveling through open space.
The characters didn't take the time to detect whether the downward force that allowed them to walk on the ship's floors was the ship's artificial gravity or that of the planet they landed on. The difference should have been measurable with a simple stepping on a scale.