When Ms.Sommers feels the stockings they glide "serpentlike" through her fingers. What does a serpent often symbolize in Western culture?

Snakes in Western culture are a symbol of sinfulness, deceit, and just general evil.

The reason for this probably goes back at least to the story of Adam and Eve.  In that, the serpent lures Eve into sin with his deceit.  So the Judeo-Christian tradition starts with a snake causing the first sin to happen.

The snake is also connected with sexual sin in particular.  This is partly because the sin of Adam and Eve is often seen as being connected with sex.  It's probably also connected to the shape of the snake and the sensuality of the way it moves.

At any rate, snakes are definitely connected with deceit and sin in our culture.