<p>Acetone can be used to smooth ABS prints.  What safety precautions should be taken during its use?</p>

There are a few main safety precautions you should consider.
Make sure the area is well-ventilated.
Acetone is flammable. A buildup of acetone gas could quickly get concentrated, meaning that a single spark could lead to disaster. Using a fan is good; angle it towards an open window. This is also to prevent exposure to acetone because of its toxicity.
Be prepared to fight a fire.
Should vapor ignite, you may need to fight the fire. If it is large enough, then you should clearly evacuate the area. If it appears to be small, use dry chemical powder to snuff out the fire. Alcohol foam, water spray, and/or fog may be used on slightly larger fires. Acetone is not likely to cause a large inferno to rip through the building. But there's always the chance of a small fire. Be careful.
Create a vapor chamber.
This is another way to stop a potential fire from spreading. It can also reduce contamination.
Wear gloves.
This can minimize any potential transfer toxic effects. However, skin exposure is unlikely to cause major issues.
Acetone is toxic, as I mentioned before, but it is not highly toxic. Exposure via
the eyes and nose/mouth
is the main risk. Skin effects may occur (e.g. mild irritation), but they are minor and generally arise only after long-term exposure (hence the recommendation of gloves in some cases).
Acetone exposure is only a serious problem when a person is repeatedly exposed to levels
greater than 1,000 ppm
(severe effects only arise at much higher levels). It seems unlikely, given a proper ventilation system, that this will be an issue
In addition to all this, basic safety precautions such as wearing a ventilator mask and goggles should definitely be taken. When working with any such chemicals with the potential for bodily harm, these should absolutely be used.