The red pickle dish isn't only a symbol of shattering and death. It's also a player in another set of symbols, all centering around the color red. The color red is often related to desire, love, seduction, sin, passion, heat, and lust. Blood, accidents, danger, warning, and alarm also factor in.
There are eight items specifically described as red in the story: Ethan's scar, the "cherry-coloured fascinator," Mattie's "cherry-coloured scarf," the notorious pickle dish, the fire, the Mattie's "crimson ribbon," and most often, the sun.
Let's focus on Ethan's gash. Many readers will instantly be reminded of Nathaniel Hawthorne's The Scarlet Letter, published in 1850, about 61 years before Ethan Frome. In that story a woman is forced to wear a scarlet (red) letter "A" on her chest to show that she commit adultery. In Ethan Frome, Ethan is similarly branded with a red mark.
If you've read our discussion of "Genre," you know this is a Gothic piece. Red is definitely a Gothic color, and Ethan's scar is a Gothic touch. The red items in Ethan Frome are related to anxieties surrounding marriage, passion, adultery, and sexuality, as well as public and private forms of shame and related emotions. All of these anxieties are placed, quite literally, on the forehead of Ethan Frome.