The insult is never named, or rather the "thousand injuries" were never named by Fortunato. We know that Montresor is an unreliable narrator because he never names the insults and his account of the entire story is so one-sided he cannot be entirely believed. Montresor tells the reader that he's tried to hide his true feelings of animosity from Fortunato when he says, "neither by word nor deed had I given Fortunato cause to doubt my good will. I continued . . . to smile in his face and he did not perceive that my smile now was at the thought of his immolation."
We do know, however, that Fortunato thinks of Montresor as a friend and has no idea the way that Montresor feels about him. We know this because Fortunato goes freely with Montresor to the catacombs beneath Montresor's estate to taste the rare amontillado. If Fortunato thought them enemies he would never have gone with him in the first place.
There was a movie made based on the Poe story in 1972 which is narrated by Vincent Price and in that version of the story the "thousand injuries" amounted to Fortunato having an affair with Montresor's beautiful wife. Ultimately the purpose of the story has little to do with the injuries and more to do with the suspense, the horror of burying a man alive behind a brick wall, the "perfect" murder.