When Odysseus and his men offer the Cyclops cheese, the soldiers with him switch positions between shots.
Telemachus is going to Sparta to see Menelaus, but the palace shown has the symbols and the colours of the Minoan palace of Knossos, which was in Crete.
After Achilles dies, he is laid on the pyre. However when we zoom in on his body, he is still breathing.
As Odysseus scales the mountain to see Circe, Hermes feeds him grass to protect him from her spells. When Odysseus first opens his mouth to eat the grass, you can tell that his mouth is already stained green from eating grass, presumably from an earlier take.
There are two babies used for the infant Telemachus. One has a head full of hair while the other is bald.
When Odysseus sees his time-worn ship half-buried in the sand on Circe's island he is overcome with grief and falls to the ground on his knees. The deep indentation of his knees is already worn into the ground before he actually kneels - either from a previous take, or to protect Armand Assante from hurting his knees.
When, after leaving Calypso's island, Odysseus is being visibly pounded by massive waves bearing the face of Posideon. However, between these shots, he appears to be totally untouched, and not even the placement of his hair has changed.
As the soldiers run down the hill as Odysseus yells "Fight, fight, fight!", one can briefly see a crew member with a blue shirt and black sunglasses standing behind them.