Plot hole: It is shown that Marge first met Luann van Houton when she was ten. But in "Homer Defined", Marge said that she first met Luann in an emergency room when Bart and Milhouse drank paint.
Margical History Tour - S15-E11
Plot hole: During the Mozart skit, Lisa puts a sleeping tonic in the emperor's wine, but when she drank it she fell asleep also. How could that be if she only poisoned one glass of wine and it was the emperor's?
Plot hole: A little ways into the episode, when Milhouse kisses Homer, he says that was the first kiss in his whole life. However, we see him kissing Samantha Stanky in the episode "Bart's Friend Falls in Love," in Season Three.
Diatribe of a Mad Housewife - S15-E10
Plot hole: Dr Marvin Monroe says to Marge he was gone for a long time because he was sick. That's impossible because he died in a previous episode and you can even see his tomb in the episode where Maud Flanders dies. [It could be argued that Monroe really was sick. It was never explained how he died and no one mentioned that he really was dead. The grave, the hospital named after him were in the simpsons universe with the belief he was dead. The clip show mentioned his death but alluded any specifics. As Marge mentions she thought he was dead and so could everyone else on the show.]
Diatribe of a Mad Housewife - S15-E10
Plot hole: When Marge is looking for inspiration for her novel, she looks at the boat painting in the TV room. On the frame, she reads it and says: "Scene from Moby Dick". Yet in "The Trouble With Trillions", Marge said that she painted it herself for Homer. So then why would she have to read the label to find out where it's from if she painted it?