Continuity mistake: In the scene where Anticlea tries to commit suicide, the sand on the beach is white. However, in a wide shot as Penelope yells "No." the sand now appears to be light brown. This shot was obviously filmed at a different time than the rest of the scene, after the tide had gone in and out.
Continuity mistake: After Menelaus reveals to Telemachus that his father is dead, Telemachus puts his hand on the green stripe on the wall, but in the closeup his hand is below this green stripe.
Plot hole: There is a wide shot of the men going off to hunt deer on Circe's island, and you can count at least ten of them. When Odysseus comes to rescue them, he sees two along the way, and then there are four in Circe's palace. Of the two back at the beach, one was changed into a pig, and the other is a human that said "Only Polites (the pig) escaped". That adds up to eight men. So at least two are missing.
Continuity mistake: When the cyclops is looking at the men's equipment, he sticks a sword into the ground. The angle of the sword changes between shots.
Visible crew/equipment: When the Trojans run out of the gates as their city burns you can see a boom mike bobbing up and down at the top of the screen.
Factual error: During the battle in the throne room, a soldier is seen hiding behind a pillar. Then Telemachus comes and swings his sword clockwise. However, we see the soldier getting hit by the sword, hitting the pillar, and then falling to the ground. This only could have happened if Telemachus had swung his sword counter-clockwise.
Audio problem: As the sailors are all running back to the ship from the cyclops' island, Eumaeus yells "What happened?", and his lips do not move.
Continuity mistake: When Telemachus is fighting with the suitor, the blood on the suitor disappears.
Continuity mistake: When the cyclops comes into the cave and says "Who are you?", we see all the men in a circle. There are nine of them. But later, when they run back to the ship, you can count at least ten of them. Even worse is that two of the men were eaten by the cyclops, so there should be only seven.
Continuity mistake: When Achilles throws the spear at Hector, there is another chariot nearby that appears to be on fire. In the next shot of Achilles we see the same chariot and the fire is gone.
Continuity mistake: The first man the cyclops eats (the one with the black beard) is standing behind Elpenor when he offers the cyclops cheese. But when the cyclops knocks Elpenor away, you can see that that man was in front of him.