Erik suffers from diabetes and says he urgently needs his insulin (which is used to lower blood glucose levels). The insulin is thrown away by one of the good guys a couple of minutes later and then Erik dies in a minute or two because his blood glucose has fallen too low (if that was the case why was he urgently needing insulin which would lower his blood glucose level?)
To be able to go outside of the aircraft and remove the engine, they would have to descend from cruising altitude down to at least 10,000 ft. Climbing back to cruising altitude would likely burn off way more fuel than they would have "saved" by removing the drag and weight of one engine. (So would staying at the low altitude).
A pilot would not contact "ground control" while airborne. The ground controllers are responsible for controlling the ground environment at an airport. At cruising altitude they would contact the en-route, center or area control.
The air in a cabin is exchanged frequently through the flight but if they want to clear the air they would open the outflow valve, not the exit door. They could have also donned oxygen and breathed it to get fresh oxygen.
An airplane does not enter a rapid descent and crash just because the engines shut down. It is still able to glide quite comfortably at a normal descent rate with no engines running.
Despite surviving a crash landing in water, somehow the remaining passengers are not soaking wet nor have bruises, internal bleeding or disorientated.
A shot of the Los Angeles skyline is incorrectly labeled as "New York City" in the movie.
Los Angles to the Island of Maui is 2490 miles, Los Angles to the island of Hawaii (The Big Island) is 2479. If fuel was so low, Kyle should have steered for the closer of the islands.