Yes. Formaldehyde and acetone are in a lot of nail products I hear.
Discussion
The formaldehyde is thankfully going away in most stuff, but, acetone... That's a sneaky one. It can cause DNA and nerve damage with constant exposure. It's EXTREMELY bioactive in humans, partly because it's such an excellent solvent. You do have some in you, naturally, but at really, really low concentrations, from what I remember. Dousing your bare skin with it all the time is very bad.