Burt finds himself captive on an alien spaceship, with a duplicate of him ready to take his place in Mary's bed; Carol's mother arrives with his newborn daughter Wendy; Jessica chooses Chester over Detective Donohue.
Mary exults about Burt's sudden resurgence in bed, unaware that he's an alien duplicate of her husband; since Wendy's mother abandoned her baby to run off with a cowboy, Jodie finds himself taking sole care of his daughter so long as his best friend Alice is out of the picture; Burt meets another captive on the spaceship, a 4000 year old Jew named Saul.
Billy is rescued from The Sunnies, after which Benson bids farewell to Jessica to work in the mansion of her cousin the Governor; Burt and Saul try to make their escape, while Mary begins to suspect that her Burt is not a different man but another man.
Jessica convinces Detective Donohue to leave; Chester falls into old habits with an old flame; Danny is rescued by Millie, the girlfriend of his wife's killer; and Billy's divorced teacher, Mrs. Leslie Walker, enjoys his flattery after confessing her loneliness.
The alien Burt prevents Mary from seeing the real Burt; Eunice admits that she can't stand Dutch; Billy takes Leslie to an out-of-the-way place where they must avoid being seen by Chester and Eunice; and the mismatched Tim and Corinne agree to divorce.
Billy spends his first evening in Leslie's apartment, meeting her condescending first husband; the real Burt is beamed back to the ship right in front of Mary, who concludes that he really can make himself invisible.
Mary's joyful pregnancy is tempered by the fear that it may turn out to be the child of alien Burt; after spending the night in bed with Leslie, the once virginal Billy admits he's finally found something better than television.
The Campbells receive a visit from Polly's family; Danny learns about Burt's illness, and suggests he leave his legacy by getting into the Guinness Book of World Records; Chester has fallen for the minister's daughter, so Jessica finally kicks him out of the house.
Jessica goes to psychiatrist Dr. Alan Posner, who keeps a punching bag in his office; Wendy's mother Carol, who jilted Jodie at the altar, makes an unannounced visit; Burt's doctor reveals he's not really dying after all; and Eunice abandons Dutch.
Danny proposes marriage to Polly; Sheriff Burt and Deputy Danny are set up for blackmail by mobster Elmore Tibbs; Dutch cannot choose between two sisters; Carol's mother joins her daughter in perjuring herself in court; Leslie now decides to kill Billy; and Jessica's death watch features a surprise visit from Benson.