Homer references the Honda Odyssey the Simpson family rented seven years ago. The Honda Odyssey was introduced in 1995, which would be seven years ago if the episode indeed takes place in 2002. However, the picture of the Honda Odyssey is of the then-current second-generation Odyssey, which was not introduced until 1999.
Every character in the “Do the Bard, Man” segment (except Krusty) dies. Here’s a list of how they all perished:
Gertrude (Marge) – Knocked herself out with a mace to avoid cleaning up the mess of bodies
Polonius (Chief Wiggum) – Killed when Hamlet stabbed him who thought he was Claudius.
Laertes (Ralph Wiggum) – Unintentionally stabbed himself when practicing his duel with Hamlet.
Ophelia (Lisa) – Jumped out a window and landed in a moat where she drowned.
Rosencarl and Guildenlenny (Carl and Lenny) – Died when they high-fived each other after being covered in poison.
Professor Frink wasn't with Odysseus' crew when they were turned into pigs by Circe. He was last seen when they went to the Island of Sirens that his glasses were broken when he saw the Sirens and crying out loud "Save me from the ladies".
A deleted scene in the Odyssey segment featured the cyclops Polyphemus, portrayed by Comic Book Guy and an extra scene with Patty and Selma as the Sirens where Patty's seashell bra tries to crawl away.
The title is a reference to the stories' copyright that have either expired or never was copyrighted to begin with. This means producers are allowed to create the stories with Simpson characters without prior consent nor royalty fees. The only exception of the theme to the song Ghostbusters, however, it's not mentioned if any fees were paid.
One of the "bills" Marge sifts through at the beginning of the episode is a death threat written in blood, presumably from Robert Terwilliger to Bart Simpson and similar to others Bob sent in "Cape Feare."
Glasses weren't invented during the time of Odyssey, yet Frink still has them.
On Channel 4 reruns, the scene, where Laertes (Ralph) stabs himself with his sword, was cut, yet no editing was done to the scene of Ralph lying dead on the floor.
The Hundred Years' War (which actually lasted for one hundred and sixteen years, 1347 to 1453) happened before the Acts of Union (where the royal thrones of England and Scotland merged to become the United Kingdom) of 1706 (Scotland) and 1707 (England); therefore, the English camp should not be flying the Union Jack (a red cross and a white saltire cross on a blue background).
It should be flying the English flag, a red cross on a white background.