As passengers begin to board a trans-Altantic flight from Boston, Massachusetts to London, UK, Jessica Fletcher (Angela Lansbury) meets several, including Gunnar Globle (Pat Harrington Jr.), who attempts to garner an audience with her to consult him about a manuscript which he has written, as he assumes an airline seat beside Jessica.
Otto Hardwick (Robert Walker Jr.) claims that he suffers from allergies to smoke, and so he exchanges seats to ride beside Errol Pogson (David Hemmings), who introduces himself to Jessica as a Scotland Yard Investigator.
Louis Metcalf (Gene Nelson) and Mrs. Metcalf (Mary Jo Catlett) conduct themselves quietly near the rear of the first class compartment, they sharing a secret which they intend to keep between them.
Celebrity actress Sonny Greer (Kate Mulgrew) boards with her bodyguard, Leon Bigard (Mark Venturini), who expresses discomfort in confined spaces especially toward an overnight flight across the Atlantic. But he's to guard her and her valuable diamond necklace, while she roams freely from deck to deck.
Airline staff includes Captain Whetsel (Chris Robinson) and flight attendants Kay Davis (Robin Dearden) and Elizabeth Welsh (Lia Sargent). Jessica perceives Kay's preoccupation with outside concerns as Kay serves Jessica's meal, selected from a rather full menu, along with an accompanying wine list, and so Jessica must remind her which wine goes with which type of entrée.
Other passengers include Fred Jenkins (Andrew Parks), Carney (Charles Hoyes), Blanton (Vince Howard), Mr. Stegmeyer (Charles Davis), and Doctor Cliff Strayhorn (John S. Ragin), who comes in handy when someone is murdered across the aisle from Jessica, and John Sukahara (James Shigeta), whose jewelry expertise comes in handy to identify the recovered stolen diamond necklace as imitation glass.
With the assistance of the crew and Otto Hardwick, who expresses romantic notions in Jessica's direction, Jessica reviews ticket booking records to discover which passengers and crew members have made last-minute reservations, when it is discovered that the two flight attendants have been seeing the same pilot in Paris.
When Jessica finally names an alleged perpetrator, the suspect confesses to the theft and the murder, and is placed in the custody of Otto Hardwick.
But as Jessica ponders the confession, she realizes a different theory and quickly places an air-to-ground telephone call to London, whispering, "Time is of the essence," as "The Corpse Flew First Class."
The cast is rounded out by Don Maharry as Mr. Miley, Crystal Jenious as Mrs. Miley, Ron Barker as The British Chief, Ian Howard as Security Man, Ron Southart as Bobby, Jim Malinda as Photographer, John Straightley as Customs Man, and Gerald York as Man on Phone.
This episode also represents the first acting credit each for Ian Howard, Don Maharry, and the most recent acting credit for Ron Southart, as well as the first of two "MSW" guest roles each for James Shigeta, Robert Walker Jr., the second of two each for Crystal Jenious, Andrew Parks, Ron Southart, John Straightley, the first of three each for Robin Dearden, Charles Hoyes, the second of three for Gerald York, the first of four for Kate Mulgrew, the second of four for Pat Harrington Jr., and the second of five "MSW" performances for Vince Howard.
In addition to Charles Davis and Gene Nelson, Mark Venturini, acting in a brief 10-year career since 1985, and David Hemmings, acting since 1954, and directing since 1972, including the next "MSW" episode, (#3.13), have unfortunately since passed.