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.

Dick crashes the car into a tree and calls an insurance company to cover it, but the salesman informs him that in order to be covered, he needed to have taken out insurance before the crash. Instead, the salesman manages to convince Harry to buy insurance, but then ignores all of Harry's attempts to call him. Dick, meanwhile, is pleasantly surprised when he discovers just how much more advanced his rental car is than the old Rambler, and so sells the latter for scrap; however, the Solomons soon begin to miss it. Guest appearances by Bob Odenkirk and Joel McCrary.

Mary invites the Solomons on a murder mystery weekend, thinking that it might prove a fun activity. However, she goes down with food poisoning and retreats upstairs to her room. Downstairs, meanwhile, the Solomons are horrified when the first murder takes place, believing it to be real and, annoyed at the apparent lackadaisical efforts of Scotland Yard detective "Inspector McAffrey" (Billy Connolly), they decide to try to solve the mystery themselves. (Cameo appearances by Andrea Martin, J. Edward McKinley, Michael Bolton, Joel McCrary, Bob Odenkirk, Terry Bradshaw, Donny Osmond, Vondie Curtis-Hall and George Carlin).

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.

At a charity auction for the Rutherford Boys Home, Dick wants everybody to applaud him and so starts a bidding war with Studwick for a painting and ends up paying seventeen hundred dollars for it. Meanwhile, Don complains when Sally's snoring keeps him up all night, so she decides to try to stay awake all night so that he can sleep, but ends up keeping him awake anyway. Back at home, Harry and Tommy have been given the job of devising a new mission statement, and so try to work out what their purpose is on Earth.

Mary is tired of spending all of her time with Dick's family and so suggests that the pair befriend another couple - her tennis partner Gwen and her husband Larry. Dick is apprehensive but quickly warms to the pair; however, they soon start brushing he and Mary off, so Dick finds them at the tennis club, where they tell him that it's because they find Mary to be tedious and self-absorbed. Meanwhile, Sally, Harry and Tommy are forced to use the laundromat when their washing machine breaks down, and immediately fall in love with the place, even setting up a laundromat court, in which Sally, imitating several of the phrases and mannerisms of Judge Judy, settles squabbles over people's washing.

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 (Lindsey McKeon) 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.

Vicki Dubcek returns with her baby Eric Travis, telling of how she has cleaned up her act and become a proper mother. Unfortunately, however, the Big Giant Head (William Shatner) decides to return to Earth and claim his son, but upon seeing Vicki with Eric, he falls in love with her and asks Dick to transform her hatred of him into love. Meanwhile, Harry admits that he is still in love with Vicki, but Dick tells him that he cannot have her because the Big Giant Head will punish him; while Tommy attempts to help Sally beat her addiction - shoes.

Dick begins to have erotic fantasies about Nina, and makes the mistake of telling Mary about it, leading to an argument between the three of them. Dick is confused, and Don explains to him that his confession makes Mary feel as if she no longer excites him. Meanwhile, Sally falls under the spell of Margaret Williams, a lifestyle guru very similar to Martha Stewart, and an impressed Mary asks her to cater for a fund raiser she is holding. However, Sally becomes annoyed when the guests do not appreciate all the hard work she has put in.

After hearing of how well his colleagues are doing in the stock market, Dick claims that he has earned enough money to share a holiday with Mary in Cancun. As a result, Dick is forced buy into the market in order to actually pay for the holiday, but he soon begins to lose money when the company he invests in is rumored on CNN to have overspent. Meanwhile, Sally cannot stand it when a tougher woman than her arrives in town, in the form of police officer Janice (Chyna). Janice and Harry, however, take to each other.

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.

It's a nice day and Dick doesn't want to be stuck in the workplace, so he decides to do something that he thinks has never been done before - fake a sick day. Mary soon finds out what he's up to and decides to join him, and the pair run into Strudwick, who is doing the same thing. Meanwhile, Sally, Harry and Tommy find a police scanner that Don has left lying around and begin listening to a woman named Andrea's phone conversations. Things take an interesting twist, however, when Harry begins dating her.

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. Guest appearance by Pat Morita.

The Big Giant Head has revealed to Dick that he is his father, and so would like to get to know 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.