It takes quite a few repeated exposures for most to have any harsh effects, but it is a neurotoxin and targets several of your organs. Through the skin you dont absorb much (more, but enough to hurt you if you work with it often enough. Inhaling the vapors is probably the worst thing to do.
"In reviewing the available data, Morgott (1993) concluded that acetone is neither a skin irritant nor a contact allergen; however, prolonged or repeated dermal exposure may defat the skin and produce dermatitis (Krasavage et al., 1982). Direct contact with the eyes may produce irritation and corneal injury (Morgott, 1993). Vapor concentrations of 300 ppm may produce slight eye irritation in some individuals (Nelson et al., 1943). "
By comparison, it takes 5 hours of inhalation of 250 ppm concentration of acetone to get you pretty screwed up (and possibly in the hospital).