Hannah's tapes are numbered in blue nail polish, and she's wearing blue nail polish the last time Clay sees her – the last day of her life. He remembers the moment:
We almost bumped into each other. But your eyes were down so you didn't know it was me. And together, we said it. "I'm sorry." [. . . ]
And there in your eyes, what was it? Sadness? Pain? You moved around me and tried pushing your hair away from your face. Your fingernails were dark blue. I watched you walk down the long hallway, with people knocking into me. But I didn't care. (14.60, 62)
Poor Clay. He had no idea that was the last time he'd see Hannah. At this point, she had already recorded the tapes and mailed them to Justin Foley. Even if she were to recognize the strong feelings Clay obviously had for her, it seems she had already made her decision. Since she uses blue nail polish to number the tapes (her last words), and she's wearing it on her last day on earth, it might symbolize the finality of her decision. Suicide is irreversible.
The nail polish might also be a symbol of the sweet, romantic girl Hannah is. She's someone who wants to paint her nails, dress up, and experience romance and love. This very typical teenaged girl quality (funky-colored nail polish) sets up a contrast with what Hannah has become. By this point in the story Hannah's heart and her girlish desires have turned blue, the color of sadness and heartbreak.