Amy asks Leela to help her buy a car at Malfunctioning Eddie's Rocket-car Emporium. Meanwhile, Bender refuses to get the recommended safety features that would reduce the risk of "catastrophic butt failure", namely explosion, in a low-speed collision installed because they make his butt look like that of a human.
Amy asks Fry to take a road trip to Mercury in her new rocket-car, but they break down after they run out of gas. While getting towed away, she and Fry begin making out.
With Valentine's Day approaching, Bender decides to start a computer dating service. Fry worries that he and Amy are spending too much time together. He asks Leela to come with them on a picnic to Europa they had planned. When she refuses, Fry asks Dr. Zoidberg out instead. Zoidberg agrees to come with them, but when Fry asks him to drive, he crashes the car. Fry wakes up to find Zoidberg telling him that his body was badly damaged in the crash. Fry, in shock, discovers that his head has been grafted onto Amy's shoulder in order to keep him alive. After returning to Earth, Fry breaks up with Amy and she makes Valentine's Day plans with another man named Gary.
Fry, Amy and Gary wind up at Elzar's Fine Cuisine, where all the people who applied to Bender's dating service, including Leela, are with their dates. However, all these dates are flops, as Bender merely rounded up a bunch of strangers from the bus station and they all leave for the bus ride home. Amy hits it off with Gary and is about to go home with him, over Fry's unwilling protestations. Luckily for Fry, Leela spots him across the room and comes over. She saves Fry by tricking Gary into talking about banking industry regulation. He soon winds up talking about various technical minutiae, distracting him from leaving with Amy. Fry quietly thanks Leela for the assistance.
The next day, Zoidberg reattaches Fry's head to his now-repaired body and everything returns to normal. Some of the nerves in Fry's neck were apparently rewired so that Fry's left leg hits him every time he touches his neck. As a result, Fry kicks Bender and his explosive butt finally blows up, saying "MY ASS! MY BEAUTIFUL ASS!".
Fry asks Leela out on a Valentine's Day date, but it's a half-hearted request and she angrily refuses. He instead goes for a ride with Amy and they end up having a short-lived affair. Fry does say in a later episode that, while he did always have feelings for Leela, he couldn't articulate them so this could be the case.
Fry's behavior towards Amy in in this episode indicates that Fry was unwilling to sustain a romantic relationship with her. In fact, he proceeded to panic when Amy said she enjoyed hanging out with him but hardly bats an eye when Leela tells him that she enjoyed hanging out with him at the end of the episode. The deliberate parallel in Amy and Leela's lines couldn't make it more obvious that we're expected to compare Fry's reactions and conclude which of the two he is willing to get serious about. Fry loves Leela. he has feelings for her. with Amy it's just fun. He doesn’t love Amy and he just got sick of her. In this episode as well as other episodes throughout the series, Fry is shown to have lower standards for looks of women for casual / no strings sex, than for relationships and pursues the beautiful Leela for a relationship but only saw Amy (who, unlike Leela, is clearly not attractive )as casual sex material.
Also in this episode, Fry is decapitated in a hovercar accident. Zoidberg attaches Fry's head to Amy's shoulder to keep him alive while Fry's body is repaired.
Bender says "Shut up, Baby! I know it!" for the first time.
The "Hg" in "Hg's Fuel" is actually the chemical symbol for Mercury.
The closet contains box files "P" and "NP", referencing the P vs. NP problem in mathematics where it's not known whether these two categories are separate.
This episode bears similarities to the ending of The SimpsonsTreehouse of Horror II segment If Only I Had a Brain, in which Mr. Burns' head is grafted onto Homer's shoulder after an accident.
The episode title may be a reference to the song of the same name by singer Paul Anka.