The 2004 film Troy was an adaptation of Homer's Iliad, covering the beginning of the Trojan War, the battles between Greece and Troy, and the internal and external fighting that plagued both sides.
One major weakness, although a specific stylistic decision made by the writer, David Benioff, was the removal of all supernatural events as depicted in the original text. The film shows all events as natural, stemming from pragmatic man instead of emotional gods, and everything happens as it might in a real war. This served the purpose of grounding the events of the Trojan War -- including the famous Trojan Horse -- in reality instead of allowing supernatural influences.
By departing from the original text, some of the mythological elements in the work are lost; for example, in the text, Paris (Alexandrus) fights Menelaus, loses, and is saved from death by the goddess Venus; in the film, there is no goddess, and it is his brother Hector who saves him and kills Menelaus -- it is interesting to note that in The Odyssey, Menelaus eventually gets Helen back, although she is not a servile wife any longer. In the text, Venus uses her saving of Paris as pretext to bring Helen to him.
...[Menelaus] was again springing upon Alexandrus to run him through with a spear, but Venus snatched him up in a moment (as a god can do), hid him under a cloud of darkness, and conveyed him to his own bedchamber.
Then she went to call Helen ... and said, “Come hither; Alexandrus says you are to go to the house; he is on his bed in his own room, radiant with beauty and dressed in gorgeous apparel."
Removal of the mythology was a conscious decision, and as such cannot be labeled a weakness as such, but it also removes much of the flavor and subtle politics inherent in the Iliad. Homer likely meant his work to be as much a satire of Greek and Roman politics as a faithful account of history, considering all the bickering, internal fighting, and backstabbing the gods engage in, and while it would not all have fit in a two-hour movie, it would have given the film a second layer of meaning.