The finishing methods explained for ABS and PLA parts require the use of some chemicals like acetone, tetrahydrofuran (THF), dichloromethane. The least dangerous one of them is known to be acetone; however, even acetone may be dangerous. It should be remembered that every chemical is potentially dangerous without special attention.
Below you will find a list regarding potential safety issues and some solution approaches. However, you should be aware that you are responsible for your own health and you should be sure to have taken all the precautionary steps to avoid possible health hazards.
Acetone: Although it is removed from the list of toxic chemicals of the Emergency Planning and Community Right-to-know Act’s section 313, it is known that it may be toxic for the kidneys and the liver. Therefore, anybody working with acetone (especially with its vapor) should avoid from smelling it. It would be OK to experiment outdoors or a good ventilated area, wearing a proper gas mask. Additionally, acetone it highly inflammable; therefore, it should be carefully watched in order not to flame.
Tetrahydrofuran (THF): It is most probably the least toxic chemical to handle the finishing of PLA. However, it can quickly dehydrate the skin; so it would be necessary to wear gloves that are not latex but nitrile or neoprene. The fumes of THF must also not be smelled, since it can cause long term effects. It is a carcinogen chemical, so, long-term exposure may cause organ damage. It is also inflammable; it should be carefully followed to prevent the working area from get burned.
Dichloromethane: According to EPA, the short-term effects of it are “nervous system effects including decreased visual, auditory, and motor functions” which can be later reversed; the long-term effects are problems in Central Nervous System. It is also carcinogen, may cause tumors in the long run. Working with it, one has to have double nitrile, PVA or viton gloves. However, it is nonflammable.
As a last comment, it would be safe to avoid breathing any of the above listed (and further) chemicals. It is also recommended to keep fire away as much as possible.