The song that Dean is humming to calm himself down on the plane is called "Some Kind of Monster" by Metallica.
When Dean and Sam are talking with Jerry Panowski about a possible poltergeist, a co-worker walks by and says: "Poltergeist (1982)? I love that movie!" This comment was added in post and was not stated during filming.
Sam mentions Flight 401 a flight that crashed in the Florida Everglades. The airline really did salvage parts and placed them in other aircraft. While the airline denies any ghost stories, it has been alleged that the dead crew have appeared on these aircraft. The airline did remove all salvaged parts from the 'haunted' aircraft.
When calling Amanda Walker in the airport, Dean introduces himself as Dr. James Hetfield, a reference to the Metallica front-man.
The airline set was completely still during the crash sequence. The effect of a plane in uncontrolled rapid descent was achieved through clever handheld camerawork.