What are some differences between the book version of "The Odyssey" and the movie version?
There are two major screen versions of Homer's The Odyssey:
The 1955 Italian film Ulysses with Kirk Douglas, 115 minutes;
The 1997 American TV Miniseries The Odyssey, 176 minutes.
Because the 1955 film is better known, I assume that is the one you are referring to.
Ulysses was filmed in 1955 in Italy, and almost every actor except Kirk Douglas speaks Italian; the original English dubbing is famous for being quite bad and mismatched. At the time, Ulysses was one of the most expensive movies ever made, and due to budget concerns, they had to shorten and modify the story.
Three major scenes are cut:
(1) Ulysses's 7-year stay on the island of Calypso
(2) Aeolus's bag of wind blowing Ulysses's ship away from the shores of Ithaca
(3) The attack of Scylla and Charybdis at sea.
Otherwise, the film is considered to be very faithful to the source material, if a bit dramatized and dumbed-down so as not to bore the audience. Most reviews mention the strong presence and charisma of Kirk Douglas, and the expensive and technologically superior (for the time) special effects. A great deal of the narrative and repetition is excised, as well as the three scenes mentioned above; they were likely cut for time and expense, as well as being the most superfluous to the plot.
One major difference between the epic poem and the 1997 television movie version of the story is that, in the movie, Odysseus fears that he will not come home from the Trojan War. He tells his wife, Penelope, that she should remarry if he is not back by the time their baby son, Telemachus, has grown up. In the poem, much is made of Penelope's obedience and loyalty to Odysseus. He never tells her to consider remarriage; in fact, he would be extremely angry had she done so. When he does return to Ithaca, he is anxious to see if she has been loyal to him in his absence, and he becomes enraged (for a moment) when he thinks that she has not (she craftily mentions a detail having to do with their old bed to test him and make sure he is really Odysseus; he passes her test). One of Penelope's defining qualities, in the poem, is her extreme loyalty in the face of all the persistent suitors that vie for her hand in marriage after Odysseus's very extended absence.