Hey there SMW. From what I understand, the possible risks and side effects for laser treatment of spider veins are roughly the same as those for any other kind of treatment that uses a laser. So on the low end of the spectrum, you might be looking at some pain during treatment (Once for an article I actually went to a dermatologist to get hit with a laser to see how much it hurt -- took a couple of shots to the face, and it stung a bit, but not so bad

), along with some redness and possible tenderness on the treatment area.
However, if you're talking about the realm of all possible risks, skin injuries, burns and scarring can occur if the laser is poorly wielded. This is why it's so important to find a treatment professional who: 1) has a good working knowledge of how a laser affects the skin and other tissues; 2) has a great deal of experience working with lasers; and 3) knows which laser should be used for each particular situation (in your case, spider veins). A conscientious practitioner will also make sure you are completely aware of all of the possible side effects and risks before they even pick up the laser to begin treatment.
Sorry if I rambled on... hope that helps a bit to answer your question!