At best, restricting blood supply with overly tight bondage causes pins and needles, and numbness. At worst, body parts are damaged, or even die without blood supply, although this would require very tight long-term bondage and it's likely it would become extremely painful before serious damage occurred. Restricting circulation is easily avoided by keeping a little slack in the ropes, ie. the one-finger rule.
However it's just as important to be aware of the effects of position changes and tension and tightness as the scene progresses. Keep an eye for ropes tightening during play, or as you build up the bondage. Insist that your partner should not try to 'tough it out' and inform you immediately of any unusual sensations, or loss of feeling, as this could be nerve-related. It's also possible that numbness could mask a more serious problem or compromised blood supply could exacerbate nerve damage.
Furthermore, if a large volume of blood is restricted, it can cause shock when the de-oxygenated blood is released. Avoid placing knots on blood vessels, for example on the inside of the wrists. Make sure you build up wide bindings to spread the load. Hands usually suffer first so, so as not to end the scene prematurely, and for safety, it's a very good idea to do your bondage so the hands can easily be released without having to untie everything.
Temperature can be a fair indicator of circulation. Note how warm your partner's hands and feet are at the start of the scene. If they become noticeably colder it's possible circulation has been restricted. Another test is to squeeze a finger or toe and see how quickly the colour returns to the nail. You'll see the nail is pink; after I squeeze it, it goes white, it then returns to the normal colour. The slower the return, the worse the circulation. A significant colour change from one side of the binding to another is a classic indication of compromised circulation. This being said, some people do seem to go purple at the slightest constriction, yet don't suffer any ill-effect; again it's a case of knowing your body and being sensible.