I agree with a number of items in the posts, particularly those items noted by copelmat. I'd like to add at least three details in the novel that haven't been addressed yet that, to me, strongly point to Hurston's interest in examining racist attitudes indirectly in her novel Their Eyes Were Watching God:
1. Janie is singled out for her light skin, yes, but she's singled out even more for her straight hair. Many of the characters in the novel react to her hair: the black women are often jealous and/or hateful, and the black men are often strongly attracted. The focus on straight hair and light skin is tied to white ideals of beauty, ideals that drove many black women in the early part of the 20th century to attempt to bleach their skin and straighten their hair through any number of cosmetic products.
2. White men, on horseback and with rifles, "enlist" Tea Cake to help bury the dead after the hurricane and flood. The dead white people get coffins, if I recall correctly, and the dead black people do not.
3. Joe Starks recreates the hierarchical structure of the slave plantation when he establishes the all-black town. He occupies the white "big house" and sets himself up more as Master than as Mayor.
Overall, the novel treats racism in ways that are mostly subtle, but subtle treatment seems to me to be a very effective strategy.