It is broad daylight when the phone is being tracked, and yet a few minutes later it is completely dark when officers arrive at the warehouse.
The dad is taped up on the warehouse floor, yet the overhead thermal image shows him sprawled out with his arms not bound.
When the 747's captain calls for pushback, the reply from ATC gives the runway in use and the words "clear for takeoff". This is nonsense, takeoff clearance is only ever given to an aircraft actually on the runway ready to go.
At 1:04, the captain instructs the first officer to contact Phoenix tower to request a landing. Airlines will not contact a tower directly when they are at cruising altitude to request a landing. They would work have to contact the approach controller and request a diversion to the nearest airport.
When the hostage-taker opens his revolver and spins the cylinder, all the rounds are seen to have been fired, i.e they have firing pin depressions in the caps.
Victoria Cruz's character is referred to as a "stewardess," a term that hasn't been used in decades. The correct modern term is "flight attendant."
The technology plot holes abound. The FBI would use secure video conferencing for a briefing in 2016, not require a supervisory agent to fly across the country. The "fix" could not work as depicted, since the LAPD would have a copy of the footage, plus deleted files can be recovered. The FBI would have no control over LAPD footage. Next, the IP address of the bad hair gun thug could be determined just by having Michelle's laptop. They did not need to wait for him to be online as stated. In the most glaring one, the son uses his cell phone to call 9-1-1. In a kidnapping case, the FBI would be tracking all phones any family member may have. The son's phone would have allowed them to find him easily. The "tech" agent says the line has to be open to trace the phone, which is wrong- as long as the phone is on, it is connected to towers and can be traced.
The entire plane scenario was unnecessary. Michelle and the bad hair gun thug could have broken in the night before and held the entire family hostage until the files were deleted with far less risk and exposure.
The FBI does not investigate murder cases. They do assist local law enforcement, but the case would have been investigated and prosecuted locally. In fact the senator's lawyer mentions the DA prosecuting the senator. If the FBI were involved it would be the US Attorney prosecuting, not the state District Attorney.
When law enforcement officers such as FBI agents fly on duty as Sarah did, they are known to the Captain, who must approve them being on the plane. Additionally, the fake badge Michelle used would have been flagged by the TSA. If it were found in her possession it would have been verified or in her case determined to be counterfeit.
Sarah as a trained FBI Agent and could have attacked the woman on the plane, made use of the other passengers and Air Marshall as needed and taken control of the laptop and phone. She could then make use of the appropriately named FBI Hostage Rescue Team to rescue her family.
The FBI boss calls for SWAT. The FBI does not have a SWAT team, they use something called a Hostage Rescue Team or HRT.
Sarah tells Peterson she saw her husband shot on camera. Her husband was off camera when the bad hair gun thug fired, so she never saw him shot.
There is no senior deputy agent rank in the FBI. Sarah's character would have been a Supervisory Special Agent. As such, she would not be involved in the rescue of her husband and son, that is the domain of the HRT agents.