When Playpen magazine arrives at Pendleton, looking for students to pose nude, Sally decides to take part. While Dick encourages this, Don is furious. Dick is horrified when he discovers that Mary posed nude for an art shoot twenty years ago, and tracks down the photographer. Harry decides to test if clothes are "all a big scam" by becoming a nudist. Tommy has his eyes on his new lab partner, Alissa Strudwick.

Dick is in a dispute with the Dubceks because Mrs. Dubcek won't fix his sink until he pays the rent, and he won't pay the rent until she fixes his sink. Eventually, Mrs. Dubcek ends up shutting off the Solomons' power, while Vicki invites Harry to move in with them. Sally has other things on her mind; after voicing to Officer Don that she is fed up with living with the other Solomons, he has proposed to her - but she doesn't know if she is ready. Meanwhile, Tommy deliberately lands himself in detention with his dream girl Alissa, so that he has a chance ask her out.

Dick begins to feel that the unit is falling apart when Sally announces her plans to move out, and he tries in vain to clip her wings. That isn't the last of his problems, however, since Harry is considering having a baby with Vicki - despite the possibility that it could turn out to be an alien. Meanwhile, Tommy sees babysitting with Alissa as an opportunity to prove to a dubious Harry that she really is his girlfriend.

Dick is up for a prestigious grant but his chances look somewhat marred when he and Mary receive chain letters, and Mary, upon throwing hers away, becomes victim to a series of misfortunes. Dick looks toward superstitious rituals and lucky charms for help. Don treats Tommy and Alissa to a series of ice hockey games for which he bought tickets for when he was dating Sally, but Tommy begins to worry that he isn't manly enough to compete with the likes of the players. Sally and Harry visit a hardware store, where Sally takes a liking to a series of workers, while Harry is mistaken for an employee, due to his bright orange shirt.

Dick realizes that he doesn't know how to use a computer and strives to learn how to use one. When he does it takes over his life and he becomes a recluse. Sally and Tommy decide to do away with their old TV in favor of a newer, better one, but end up becoming addicted, wanting all the latest features. Harry and Vicki, however, are trying to get pregnant, but the medical-science part of it is turning Harry off.

Dick, Tommy, and Harry begin to notice that, since Sally moved out, their apartment has become filthy. Mary suggests that Dick hires her maid part time, but, to her annoyance, Dick ends up stealing her full time. When Sally finds out that she has been replaced, she is hurt. Tommy has managed to get himself in charge of the school newspaper, but he becomes so dedicated to printing the absolute truth that he begin to worry school officials and even alienate his girlfriend Alissa.

Dick is jealous when fellow physics professor Vincent Strudwick publishes a critically acclaimed, bestselling book on physics, and, while Mary busies herself showing the visiting Nobel Prize winners around the campus, he decides to write a second book that will better Strudwick's. He then realizes, however, that he cannot publish all the secrets of the universe without raising unwanted questions, and so looks for another way to get at Strudwick, using Tommy and Alissa - who, it turns out, is Strudwick's daughter. Sally and Don decide to start hanging out as friends, but soon find themselves unable to resist each other.

When Sally, Harry and Tommy are nearly crushed by a chandelier in a restaurant, they feel reborn, as if they are discovering everything for the first time. Dick is jealous, however, and while Sally and Harry volunteer themselves at a homeless shelter, he strives to have a near-death experience so that he might enjoy life like they do - and a faculty trip into the mountains presents itself as the perfect opportunity. Meanwhile, Tommy decides to waste no more time in his life - and asks Alissa to marry him.

The Big Giant Head sends a message that he intends to visit Earth, so Dick quickly orders Sally to move back in and Harry to stop attempting to make a baby with Vicki. He then attempts to prepare Mary for his visit by telling her that an 'old college chum' is visiting and that she would be well advised to discuss how much he has learned in bed. Harry tries his best to avoid Vicki, but eventually resorts to telling her that he can't father a child with her right now. When the Big Giant Head arrives on Earth, he is unimpressed with Dick, his leadership skills and his choice of girlfriend, while being impressed with Sally, her style, and her body.

Dick is suffering the humiliation of having been demoted from High Commander to Harry's assistant, performing the most menial jobs, while Sally has been promoted to his old role. Tommy is preparing for his high school prom with Alissa, but when the Big Giant Head insists on coming, things start to slide, especially when Vicki, who missed out on her own high school prom, turns up. After ruining the prom for Tommy and Alissa, the Big Giant Head whisks Vicki off to his bachelor pod in space.

When a drunk Mary tells Dick she once had a fling with his archenemy Vincent Strudwick, he is outraged and decides to get even with the pair of them by convincing Strudwick's wife to sleep with him. Tommy supports Dick's decision, imagining double dates - himself with Alissa and Dick with Strudwick's wife. Meanwhile, Sally gets the hots for Don after he starts riding a police motorbike, but the pair crash and Don ends up in full body plaster.

When Mary and Nina talk about how good looking Harrison Ford is, Dick decides that he himself is hideous and visits a plastic surgeon to discuss having his face surgically altered. However, when the surgeon tells Sally that she might benefit from having some plastic surgery herself, she becomes paranoid and believes herself not to be good enough for Don. Harry, meanwhile, is chuffed when the surgeon tells him that his face is perfect.

Dick is confused when Nina won't let him accompany her to her Black Student Union meeting, believing it to be a Weight Watchers type club; so, in an attempt to understand the concept, he mistakenly takes the Solomons to a racist white power rally. Dick realizes that the rally was a bad idea, and tries to make it up to Nina by firing her, to release her from what he calls her 'servile role' (as he and Mary's assistant), but she informs him that she is happy in her job. Meanwhile, Sally, Harry and Tommy are preparing to take part in a poetry competition and decide to use racism as their subject.

Mary reveals to Dick that she has been observing his family for a number of years and that she would like to make a documentary about them, in order to show how the 'typical American family' has changed. Unfortunately, Mary's film soon begins to create tension among the family and accusations that Dick is an abusive father, Tommy is a bed-wetter and Sally is secretly a lesbian start flying around, so Harry decides to become an alcoholic so as not to be left out.

Valentines Day is approaching and Tommy hopes to get a hotel room and lose his virginity to Alissa, however, he is nervous when he discovers that she is sexually experienced and so loses his virginity to Mary's niece Tiffany first. Meanwhile, Dick discovers that Mary is seeing a therapist and, paranoid, he starts seeing her too, in order to find out what Mary has been saying about him. Paranoia fills Sally also, when Don gives her a gift which he teasingly says is from her 'secret admirer', and she mistakenly believes she has a stalker.

Pendelton University has a new chancellor, who causes anger when he cuts funding and takes away tenure, so Dick holds a meeting, in which he convinces the faculty to resign en masse. Unfortunately, the chancellor accepts the resignations and leaves everybody in the faculty, bar Dick - who withdrew his own, without a job. Upon finding out about his betrayal, the faculty protest outside Dick's classroom and Mary refuses to be seen with him. Meanwhile, Tommy begins working at a pretzel store with his girlfriend Alissa, but begins to dislike working with her and gives Sally and Harry free pretzels, with which they start their own business right in front of the store.

Dick and Mary are getting ready for the annual Rutherford Badger Day Dance Contest, but there's a small problem - Mary can't dance. Harry however has teamed up with Nina, but when Dick sees just how good a dancer she is, he orders Harry to let him dance with her instead. Meanwhile, Tommy and Don become exasperated when Alissa and Sally become friends and try on nearly everything in the clothes store. Jealousy arises, however, when Tommy discovers that Sally saw Alissa naked in the changing room, and then Sally discovers that Alissa accidentally walked in on Don changing in the Solomons' toilet. After Dick (and Nina) win the dance competition, the episode closes with a wordless pas de deux, complete with orchestral accompaniment of George Gershwin's "He Loves and She Loves", in a tribute to the final scene of the 1957 film Funny Face starring Fred Astaire and Audrey Hepburn. A portion of the film's choreography is re-created by Dick and Mary.

Dick and Harry fall into a large hole in the woods, which covers over when they attempt to climb out. Dick then panics, whilst Harry remains in a relaxed, zen-like state. A hole expert, named Angus 'The Hole' McDuff is called to the scene and devises a plan to build a second hole in order to access the one Dick and Harry are stuck in; however he becomes highly offended when Sally belittles his idea.

The Big Giant Head and his new wife Vicki Dubcek arrive back on Earth, where the Big Giant Head takes Dick to a jazz club and admits that his marriage is troubled, and that he would like to get to know him better. As his overlord becomes increasingly more clingy, Dick begins to wonder what the reason behind it is. Meanwhile, Sally gets the wrong idea when she hears Alissa giving Tommy advice about his Valedictorian speech, and saying that it is a time to move on, and so, thinking that Tommy is about to get dumped, she finds Alissa and breaks up with her on his behalf. Harry finally asks Janice out on a date and the pair get together after a meal at the gym; however, Vicki is jealous, her old love for Harry stirring admits her troubled marriage.

The Big Giant Head has revealed to Dick that he is his father, and so would like to get to know his girlfriend Mary better; however, Mary gets drunk at the dinner party and reveals that she has slept with over forty men in her lifetime. The Big Giant Head orders Dick to break up with Mary so he decides to run away with her, before Tommy reminds him that Earth children defy their parents all the time. Meanwhile, Vicki invites Harry's new girlfriend Janice to Tommy's graduation, where she attempts to kill her from beneath the bleachers; however, Sally quickly realizes what's going on and rushes to intervene before it is too late. The time comes for Tommy's speech, but he puts aside talking about his achievements to try to convince Alissa to forgive him.

Tommy is still reeling from his breakup with Alissa, but Sally and Harry convince him that if he can find an excuse to go over to her house, he can persuade her to watch a movie with him. When the pair leave the house together, however, Strudwick is suspicious and confronts Dick. Mrs. Dubcek suggests that they could have eloped, so Dick and Strudwick rush off to track them down before there's a baby on the scene, managing to accidentally abandon Mary in the process. Meanwhile, Tommy has rented a scary movie to watch with Alissa, in the hope that it might bring her into his arms, but Sally and Harry decide to show up and make it more real.