It might be worth looking at "I Could See the Smallest Things" in a little more detail, though one of the other answers to the question addresses that story, as well. In "Smallest Things," a character named Nancy alludes to an alcohol-fueled feud between her husband, Cliff, and their neighbor, Sam. During the course of the story, we begin to understand that Sam has stopped drinking, but Cliff has not, as he seems to spend the story deeply asleep in bed, apparently having passed out after drinking. While the conflict underlying this story seems to be Sam and Cliff's argument, there is a subtle disconnect between Nancy and Cliff. Nancy is the narrator of the story and appears to still interact with the world in a normal fashion, while Cliff obliviously slumbers in the background, lost in an alcoholic stupor. On the final page, Nancy imagines that her husband's fitful snores are similar to the slugs Sam was killing out in the yard, and thus we get a sense that all is not well within Nancy and Cliff's marriage, and that Cliff's alcohol use has begun to drive a wedge in their relationship.
From my answer and previous answers to this question, we can see that alcoholism, or at least drinking too much alcohol, is a common theme in Carver's stories, and he often explores the topic as a way of also exploring familial relationships that have broken down or that are in the process of breaking down. Often, Carver's allusion to the damaging aspects of alcoholism is subtle in the extreme (a result of his trademark minimalism), but it is perhaps this subtlety that makes Carver's writing so brilliant. We can tell that alcohol use is disrupting familial relationships and friendships in "Smallest Things" and other stories, but we can only tell through hints and suggestions, making the problem of alcohol use even more haunting.