When the children hear Lily curse, they become worried that they have been a bad influence on her.
As the kids are enjoying themselves in the living room, Rita and Lynn Sr. are heading off to the mall, because Dr. Shuttleworth of the Daycare Academy, is coming to interview Lily, and Lynn Sr. needs a more appropriate tie. Once they head out, Lynn changes the TV channel, because Dessert Storm is on right now, and Lily suddenly exclaims "dannit." This causes her siblings to gasp in horror, because they think that Lily has just said the "D" word. The siblings fear that Lily learned the word from them, because in past experiences, the kids have gotten into some predicaments that led them to crying out the "D" word in anger (or in Lana's case, pain), and Lily was there to witness them saying it. Because of this, the siblings are worried about potentially being a bad influence on Lily, and fear that if Lily says the "D" word in front of Dr. Shuttleworth during the interview, she won't get accepted into the daycare academy she runs. After opposing Lisa's idea of removing Lily's vocal cords, Lincoln comes up with a much better and safer idea: if Lily imitates their bad behavior, they should come up with better (and nicer) behaviors for her to imitate, and that way she won't say the "D" word in front of Dr. Shuttleworth (and possibly their parents).
The plan is set into action. Each of the siblings are tasked on reenacting the action that led them into saying the word. Throughout all of these, their faces would turn red, and are on the verge of saying the word, but they would say something else in hopes that Lily would mimic them. After nearly an hour of doing these actions, the siblings believe that Lily has forgotten all about the word. At that moment, Rita and Lynn Sr. arrives back, and begin prepping things up for Dr. Shuttleworth's arrival. One of the things they do is set a tray of snacks on the table. Lily tries to get one, but Lori tells her the snacks are not for Lily, causing her to exclaim "dannit" again, making the siblings realize that the plan didn't work.
Dr. Shuttleworth arrives, and is ready to interview Lily. Dr. Shuttleworth gives Lily several things to play with, such as a hardware set, a guitar, and a ball, but the siblings fear that Lily would do something that could lead to her yelling out the word, prompting them to confiscate the toys. When the kids become too bothersome with their meddling behavior, the parents tell the kids to leave, but Dr. Shuttleworth tells them that they should leave too, as she just wants to be with Lily. The siblings huddle up, and says that they need a plan to get Lily out of the room. Lincoln suggests on making Lisa take Lily's place, because of the fact that she wears a wig after a nuclear experiment gone wrong, and wearing dentures. Luan takes Lily away under the guise that she soiled her diaper, and put Lisa, disguised as Lily, in Lily's place. However, Lisa begins displaying some of her smart-aleck attitude, like painting complex formulaic equations, doing an impressive xylophone solo, and able to tell Dr. Shuttleworth what type of condition her eyes are in, just by looking at her glasses. This prompts Luna to tell Lisa that she needs to act more like a 1 year old, which she does by intentionally soiling her diaper.
Later, Dr. Shuttleworth is done interviewing Lily, and concludes that due to the things Lisa did, she's allowed into the academy. Just before Dr. Shuttleworth leaves, she takes the snacks on the table with her, causing Lily to exclaim "dannit." Everybody is left horrified at this action, and the remaining siblings come to her defense by pleadingly explaining to Dr. Shuttleworth that Lily didn't mean to say that word, and say that they've been a bad influence on her. Dr. Shuttleworth, however, laughs at this, explaining to them that Lily wasn't saying the "D" word--according to Dr. Shuttleworth, Lily was apparently just trying to say "doughnut," and with some help, Lily pronounces the word correctly after being given a doughnut by the doctor.
After Dr. Shuttleworth leaves, Lynn Sr. and Rita start cheering about Lily getting into the daycare academy, while the kids are glad at the fact that they apparently weren't a bad influence on their youngest sibling. However, as they cheer, Charles comes by, and snatches Lily's doughnut out of her hand, causing Lily to cry out an actual, more offensive curse word in fury (which is bleeped out), causing the family to look on and gasp in sheer horror.
This is the second episode that involves swearing, and there was a brief joke about it in "Get the Message".
This episode likely takes place after "Making the Grade", because Lisa could see well without glasses.
The song Lisa raps to get Lily to mimic her from saying the "D" word is the Blarney the Dinosaur theme, first heard in "For Bros About to Rock".
Apparently, due to some experiments-gone-wrong (one of which being a nuclear experiment), Lisa:
Is bald, and has to wear a wig.
Has an extra toe on one of her feet.
Has to wear false teeth.
The closed captioning for the episode shows that Lily said "dannit.", before her actual saying is revealed.
If one looks at the siblings' lips, they weren't saying "dannit". They were saying the actual "D" word.
Incidents that caused Lily's siblings to openly yell out the "D" word in front of her, as well as the sound that blocked off their shouting of the word:
Lincoln - Accidentally broke the TV; the TV breaking.
Lori and Leni - Ripped a sweater that they were fighting over; the washing machine buzzing.
Luna - Broke one of her guitar strings; a loud guitar riff.
Lynn - Her baseball landed in the neighbor's yard and, presumably, got destroyed by a lawnmower; the lawnmower whirring.
Lana - Banged her hammer against her hand; Lola honking the horn on her Princess Car.
Lola - Crashed her Princess Car; the airbag deploying.
Lisa - Sang a rap song that had the word; a squeaky toy.
Luan and Lucy were the only siblings not shown to have said the "D" word (possibly off-screen).
Lori and Bobby have apparently been dating for two years prior to this episode; Lori states that the sweater she and Leni were fighting over was given to her by Bobby for their second anniversary.
This is meant to be the first episode to show that Lisa is bald and wears a wig (as shown by Lincoln's reaction to learning it), but "Room with a Feud", which also shows this, aired before this episode.
There are clues that indicate that Lily was actually saying "doughnut":
When Lynn changes the channel to Operation: Dessert Storm, the cover title has doughnuts on it.
Lily attempted to get a doughnut from the snack plate, but Lori took her away and said that it was meant for Dr. Shuttleworth.
Lily was reaching out for Dr. Shuttleworth's purse, which had a doughnut.
It's possible that at the end of the episode, Lily may have said what's referred to as the "F-bomb" (or possibly the actual "D" word, or possibly the other one).
However, based on the way she moved her mouth, it is unlikely for her to have said the "D" word, since it would require her to open her mouth twice, when clearly she did only once.
In this episode, Lisa wears a surgeon's outfit similar to the one in this episode's sister episode "L is for Love", albeit with a few differences.
In the Hebrew title card for the episode, the red "?#@*%!" in Lily's mouth is not present.
Potty Mouth - The title of this episode is a phrase that refers to a person who likes to swear/curse.
Grawlixes - The random characters used to cover up Lily's swearing on the title card are known as grawlixes, which are "typographical symbols standing for profanities, appearing in dialogue balloons in place of actual dialogue".
Wii - The game remote Lincoln was using in his flashback of yelling out the "D" word highly resembles a Wii Remote (Wiimote), and the joke of Lincoln accidentally tossing the remote into the TV is a reference to how most people who own Wiis damage their TVs or surrounding walls due to neglecting the use of the remote's wrist strap.
Daniel Day-Lewis - After crashing her car again, Lola mentions the actor by name as a euphemism for the "D" word.