Although I would disagree with the strategy of teachers who send their students off in search of tragic flaws (this approach is worn out and old fashioned), I would say that there are a couple of points in Homer's Odyssey where Odysseus makes critical mistakes.
On two occasions, Odysseus falls asleep. Surely it is not pride that makes him fall asleep. Once, in Book 10, when he falls asleep and his men open the bag of winds, which blow them away from Ithaca. The next instance of sleep comes in Book 12, when he falls asleep on Thrinacia, his men eat the cattle of Helios, and this god's anger brings about their destruction and in Odysseus being shipwrecked on Calypso's isle. Where is Odysseus' pride in these scenes?
If one is looking for pride, though, Odyssey 9 is probably the best place to look, and these two instances frame his encounter with the Cyclops. After Odysseus and his men go to the Cyclops' cave and find that the creature is not there, Odysseus' men want to take some food and leave. Odysseus, however, does not take his men's advice:
But I would not listen, though it would have been best, wishing to see the giant himself, and test his hospitality. (A.S. Kline translation)
This decision results in the deaths of six of Odysseus' men, whom the Cyclops eats.
Near the end of Odyssey 9, after Odysseus escapes from the Cyclops' cave, Odysseus makes his next mistake, which is a result of something closer to what might be classified as pride. This mistake is the revelation of his real name to the Cyclops.
So they argued, but could not daunt my ardent spirit, and I shouted to him again in anger: “Cyclops, if any man asks how you came by your blindness, say that Odysseus, sacker of cities, Laertes’ son, a native of Ithaca, maimed you.”
This information allows the Cyclops to pray to his father Poseidon, who causes Odysseus to be shipwrecked after he leaves Calypso's island.
Thus, if Odysseus does exhibit destructive pride, it seems to me that these two places in Odyssey 9 might be considered examples of it.
I think the 2nd one was more helpful then the first, beucase the first is not in the version i am reading!