Ulysses, in beggar's disguise, is granted permission to draw the bow. As he takes it and moves to another spot to string it, a metal wristband suddenly materializes on his left arm where a few seconds before there was none.
The inconsistent position of Circe's veil on the kissing scene when see from different angles.
When Ulysses and his men crush the grapes to make wine for Poliphemus, Ulysses gives the juice directly to him. It hasn't had time to ferment. So, Poliphemus is getting drunk from just grape juice.
Ulysses, being Greek, would have referred to the god of the sea as Poseidon, not Neptune. Neptune was the Roman name for the god of the sea. (Anyway, Ulysses itself is the Roman name of Odysseus.)
There are inconsistencies of scale with the giant Polyphemus: for instance a human scale wineskin is nearly as big in his hand as the sailor he devours.
Antinoos 'fails' to string the bow of Ulysses but it is clear that he has bent the bow enough and an effortless movement of the looped string would have been all that was required.