Amy asks Leela to help her buy a car at Malfunctioning Eddie's Rocket-car Emporium. Meanwhile, Bender decides not to get the recommended safety features installed these would reduce the risk of "catastrophic butt failure," namely explosion, in a low-speed collision, but it makes his butt look Human.
Amy asks Fry to take a road trip to Mercury, but they break down after they run out of gas. While getting towed, 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 to instead. Zoidberg comes 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 his head is grafted onto Amy's shoulder in order to be kept alive. After returning to Earth Fry breaks up with Amy and she makes Valentine's Day plans with another man, Gary.
Fry, Amy and Amy's date wind up at ElzarFine 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 her date 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 Amy's boyfriend 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 is still not in love with Leela. He asks her out for 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. Also in this episode, Fry is decapitated in a hover car accident: Zoidberg attaches Fry's head to Amy's shoulder to keep it alive while Fry's body is repaired. Bender says, "Shut up, Baby, I know it!" for the first time.
In "Hg's Fuel", Hg is 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 mirrors the The Simpsons episode Treehouse of Horror XXIV, Dead and Shoulders segment where Mr. Burns' head is a part of Homer's body, where in this episode Fry is a part of Amy's body.
The episode title may be a reference to the song of the same name, by singer Paul Anka.