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. 

All of the stories show characters who are unable to talk about their feelings in a productive way.  In the title story, the most prominent indicator of dysfunction is alcohol. The characters talk about love as they drink, but we learn through the stories they tell they have difficulty forming substantial relationships. When Mel says “Gin’s gone,” his wife answers “now what?”—meaning what do they say and do without the gin. These characters almost fail to exist without the alcohol.  In “Gazebo” Holly and Duane have arrived at an impasse because of Duane’s infidelity. He and Holly try to get past the issue by getting drunk and making love, but her trust has been shattered and silence engulfs them. In “So Much Water So Close to Home” Claire feels herself drowning in emotions that are too murky for Stuart fully to understand.  In “I Could See the Smallest Things,” a woman’s husband is passed out in their bed, and she wanders into the backyard in her robe, and talks to her neighbor who is also up, pouring poison on slugs.  They talk but say little, even though it is clear the woman is feeling something she can’t put into words about the awful desolation of her life, her loneliness, her lousy marriage.She has no epiphany about this, but merely goes back to bed thinking “I didn’t have anymore thoughts except the thought that I had to hurry up and sleep.”

Mel and Terri in "What We Talk About When We Talk About Love", exhibit a variety of familial dysfunctions.  Terri, an extreme romanticist, has allowed herself to be a victim of abuse in her first marriage, and is insistent that love for her was behind her ex-husband's violence and ultimate suicide.  Mel admittedly does not understand what love is.  He speaks about wanting to be a knight because "you are pretty safe wearing all that armor", and describes a beekeeper's "helmet...big gloves...padded coat".  Both images are symbolic of the emotional armor behind which he hides.

Another familial dysfunction evident in that story, and also in "Cathedral", is a dependence on alcohol. The narrator in "Cathedral" blithely describes drinking as "one of our pastimes"; in both stories conversation develops hand in hand with progressive drunkenness.  Alcohol covers the characters' inability to communicate, to hear and understand each other.