What are the stengths and weakness of the film Troy as the means of understanding of the period of the Trojan war?
This is a far more complex question that you might expect. It is important to know that scholars debate what time period Homer's Iliad reflects. Some say that Homer's epic describes the Bronze Age, others say that dark ages of Greece (10th and 9th centuries), and still other say that the epic reflect many different ages as the composition of the work has come down from various ages. So, there is little consensus of the historical background of Homer's Iliad. In light of this, we can say that the movie Troy cannot possibly do justice to historical questions. Even the scholars disagree!
However, what the movie does well is develop the values of ancient Greece. First, it shows that there was a dynamic of seeking honor and glory among the Greeks. For example, Achilles fought for glory and his honor, not the honor of Agamemnon.
Second, the movie also does a great job with the portrayal of characters. Paris does comes off as weak fighter who is effeminate. Hector does come off as a great and honorable warrior as Homer does. Achilles comes off a godlike in his martial prowess, and his hatred for Agamemnon is spot one.