Some things are said to be flammable and this just smells flammable. Don't be a hero and open up a can of it in your room with the doors and windows closed. Go outside. If you must open it indoors (a room, a garage, etc) at least make sure there is a lot of ventilation with a couple fans blowing around and the windows open.
Acetone is volatile but as long as used in a properly ventilated room away from all ignition sources, then you should have no problems. It is not necessarily harmful to you but it is intoxicating and will depress the central nervous system if inhaled in copious amounts.
There was some residue left behind but it looked like water. It was odorless and didn't feel oily
It was possibly water, even reagent grade acetone is about 0.5% water. However, I would recommend letting it thoroughly evaporate and then check for residue. If it was water then it should evaporate in a couple hours.
I pulled out the coins, dried them off with canned air, and set them on some wristwatch paper. The acetone almost ate through the gloves and the gloves just barely survived.
In the case of an obviously "dirty" coin and even in the case of any coin, I would recommend a clean rinse after the soak. Nitrile does not hold up too well to acetone but I believe that chloroprene gloves work ok. I do not wear gloves at all and acetone is relatively harmless to the skin although it will strip all essential oils making your skin very dry so minimize contact but you do not have to avoid it.