1. Who took this photo of Homer in outer space?
2. If Mr. Smithers was allergic to bees, why did he make Homer "head bee guy?"
3. Whatever happened to the family rumpus room?
4. Why didn't Moe ever recognize Bart's voice?
5. Why is Lisa playing a blue sax in the intro, when her sax is golden in the series?
6. Why was Ralph in Bart's class during certain episodes and in Lisa's class during others?
7. How did the Simpsons take a trip to Washington D.C. if Marge had a childhood fear of flying?
In "Mr. Lisa Goes to Washington" the Simpsons take a flight to Washington D.C. for Lisa's speech, but in "Fear of Flying" it's revealed that Marge is actually terrified of planes.
8. How did Bart get passed up for Fallout Boy when Milhouse is clearly the same height?
In "Radioactive Man," the film's director claims that Bart is an inch too short to play Fallout Boy. Milhouse might be tall, but there's no way he's an inch taller than Bart.
9. Lisa claims Luke was her first crush... But what about Mr. Bergstrom?
She also leaves out Nelson, Thelonius, and the boy from the library in "Bart's Girlfriend."
10. If there wasn't enough room in the fallout shelter, how did Ned easily walk up to his family and then outside?
There are too many people in the shelter when Homer is trying to shut the door, yet somehow Ned is able to say goodbye and give Todd a loaded shotgun.
11. Why was Mr. Smithers black in only one episode?
His hair color was also changed from blue to grey.
12. How did Homer escape the duel at his childhood farmhouse if he and Grandpa Simpson burned it down?
13. How did Santa's Little Helper bury the "replacement Homer" head in the backyard if he didn't live with the Simpsons until after the B-Sharps broke up?
14. How did Dr. Marvin Monroe reappear if his character died earlier in the series?
In "Diatribe of a Mad Housewife," Dr. Marvin Monroe tells Marge he was gone for a while because he was "sick." However, in the episode where Maud Flanders dies, "Alone Again, Natura-Diddily," you can see his tombstone.
15. If the characters' ages never change, why is Mr. Burns 81 in one episode and 104 in another?
In "Simpson and Delilah" he's supposedly 81, but in "Who Shot Mr. Burns?" he's 104.
16. If Homer started firing blanks after working in the nuclear power plant, why is Marge still taking birth control?
In "Brother, Can You Spare Two Dimes" Homer is revealed to be sterile as a side effect of working at the nuclear power plant, but in "O Brother, Where Bart Thou?" we see Bart switching out Marge's birth control with Tic Tacs.
17. When did Barney start drinking again after he became sober?
18. Why did Agnes Skinner complain about Seymour kicking her in the womb during the Olympics if he's actually Armin Tamzarian?
19. Why does Milhouse say Homer was his first kiss if he made out with Samantha Stanky in season three?
Milhouse makes out with Homer in "The Way We Weren't" and claims Homer was his first kiss... Maybe he forgot that he locked lips with Samantha Stanky in "Bart's Friend Falls in Love."
20. Why was Apu so excited about jury duty if he's already served on one?
At the end of "Much Apu About Nothing" Apu is elated to hear he's been chosen for jury duty. Which is strange considering he was already a jury member in "The Boy Who Knew Too Much."
21. Why does Moe say that no women have been to his bar since 1979 if he hired a female waitress in "Flaming Moe's?"
Also, in "New Kid on the Block" and "Homer the Vigilante," Ruth Powers is shown ordering a beer at the bar, and even Marge pays Moe a visit in "Bart Gets Hit by a Car."