After rewatching O Brother, Where Art Thou?, I realized the irony of the governor being named after Menelaus, Helen's husband from The Iliad. The Menelaus of lore started the Trojan War, the reason why Odysseus left home in the first place, but the Menelaus of the film pardons our heroes and gives them legitimate work, allowing them to come home. - Slacker Spice
Wait, who? The Governor was "Pappy" O'Daniel and they named the character after the former Governor of Texas.
It gets maybe one mention, when the audience hears the sign off of his radio show, but the governor's name is Menelaus "Pappy" O'Daniel.
The governor also underscores another Odyssey reference: after Odysseus returned to Ithaca, he had to re-establish his right to rule as king against a populace that resented him for murdering two generations of their sons (first as soldiers to Troy, then as suitors to Penelope.) Everett can't be the mayor of his hometown, but he does inadvertently help the governor of Mississippi get reelected. It's the opposite of a Composite Character.
For the longest time, I was also confused about Everett asking the hobos if they had ever been smithies. Then I remembered that they were chained together, and realized that yeah, a smith might be a good idea, especially after what happens next.
There's a joke in this movie so subtle it took me years to realize it, and I'm convinced it goes over most people's heads. The John Goodman character is obviously based on the cyclops. We later find out that he's a member of the Klan. One of the ranks in the Klan is Grand Cyclops.
Really, the Odyssey references are astounding. The blind seer, the punishment for killing (the Sun god's) cattle, the mysterious and dangerous Sirens, animal transformation, Cyclops... even Everett's wife's insistence on having the perfect, precise wedding ring from their old house: Penelope did not believe Odysseus until he proved himself to her by telling the story of how he made their unique and one-of-a-kind wedding bed.
The scene in the movie theater is meant to represent Odysseus' journey to the underworld, where he is given a warning by the spirits of the dead (in this case Pete, who they previously assumed had been turned into a toad and squashed, warns them not to seek the treasure).
The term "odyssey" in the original Greek can be roughly translated to "Constant Sorrow" which is aptly, the title of the song that identifies our heroes.
At the climax, Homer Stokes is run out of town on a rail. This is the traditional prelude to a being tarred and feathered — ironically, he's going to be lynched himself.
The Odyssey references in this are amazing...
The singing women in the river are either Sirens or Lotus-Eaters. Explicitly called "sirens" but distracted the heroes and put them in a stupor.
Delmar: Them si-reens did this to Pete! They loved 'im up and turned him into a horny toad!
They're the Sirens. Everett should have tied himself to the steering wheel of the car. They also get a role as Circe, the sorceress who turned men into pigs. The Lotus Eaters are represented by the people being mass-Baptized in the river.
The KKK rally is the scene where Odysseus and his men have to sneak out of the Cyclops' cave dressed as sheep.
The name Peter (Pete) means "the rock". The name Delmar means "(of) the sea". Everett is stuck between THE ROCK and THE SEA, referencing Charybdis and Scylla.