In Poe's "The Cask of Amontillado," nearly every part of Montressor's plan of revenge goes according to schedule, so there are not too many complications from his angle. The only real snag is for the reader, as we are not in on the plan from the beginning. We are like Fortunato, oblivious to the plan of revenge.
Getting Fortunato into his catacombs is easy: the amontillado does the trick. The complication, I guess, comes in making him walk deeper and deeper into its dark passages.
For the reader, the complication comes when Fortunato debates turning back. Fortunato is ill with a bad cough, and the nitre of the catacombs only makes it worse. Even Montressor beckons him to return:
"Come," I said, with decision, "we will go back; your health is precious. You are rich, respected, admired, beloved; you are happy, as once I was. You are a man to be missed. For me it is no matter. We will go back; you will be ill, and I cannot be responsible. Besides, there is Luchesi-"
This, of course, is really part of the plan, verbal irony by Montresor scripted to make it seem like he is a friend who cares about his health. This bit of reverse psychology is the only complication I can see.
One definition of the term "complication" is that it is "A series of difficulties forming the central action in a narrative." If we use this definition, I would say that the main complication is how Montresor gets Fortunato to follow him down into the cellar where Montresor will wall him up and kill him.
Montresor has his plan for how to kill Fortunato slowly. But first he has to get him down into the cellar. How he gets Fortunato there makes up most of the story. So I would say that that is the complication.