In "The Cask of Amontillado," there are many things missing in the video, and several changes as well.
One early and obviously difference that struck me was the change of the word "nitre," which is a mineral deposit accumulating on the walls of the catacombs. In the video, it is referred to on several occasions as "mold."
Poe uses the word "motley" to describe Fortunato's costume, which is that of a jester, but the word is not used in the video.
Another major difference is Montresor's reason for why his palazzo (house) is empty. In the story he tells the servants they may NOT leave the house to join in the Carnival festivities, when he knows full well that by telling them not to go, they will go, and the palazzo with be empty, so there will be no witnesses to his evil plan. This is mentioned in the story, but not in the video.
In the catacombs, Fortunato makes a gesture that is a secret sign of the Freemasons. He is slightly snobbish in believing that Montresor has no idea what it refers to—inferring perhaps that this secret society is above Montresor's social standing. When Fortunato speaks of the masons, Montresor pulls out a trowel to use with the plaster, making a joke, which makes no sense to Fortunato, also missing in video.
In terms of the setting, in the short story, the entire narrative and dialogue seem to lead us down into the catacombs, but in the Vincent Price version, it is told by Montresor without even leaving his dining room table (an interesting perception). I don't know if there is anything to refute that this could not have been the case: Montresor is, after all, telling the story many years after.
When Montresor chains Fortunato to the wall, the video version states that he seals him behind the wall, and the story ends there. The reason the short story is, in my opinion, so much more effective, is because Fortunato starts to come out of his drunken stupor, and pleads with Montresor, "For the love of God, Montresor!"
Because the video ends so abruptly, there are many other things left out. There is a part at the end of the short story where Fortunato laughs hysterically after being imprisoned. And just before Montresor seals the last stone in place, there has been silence for so long, that he puts his sword inside the hole to see if he can get some kind of response from poor Fortunato. In the short story, the last thing we hear, with the setting of the final stone, is the tinkling of the bells on Fortunato's hat (which is not in the video), Montresor's assurance that Fortunato has remained undisturbed in this place for the past fifty years, and the murderer's last words, "May he rest in peace."