The most obvious hazard to both falling and fainting are impact injuries through striking the floor or other objects on the way down. However bondage carries addition risks; be very careful what you tie to fixed or heavy objects, for example to consequences of tying piercings in this way and falling can be very unpleasant, and genitals don't even bear thinking about!
In order to minimise the risk of fainting you should make sure your partner has eaten fairly recently and doesn't become dehydrated. Energy drinks and water and snacks are good to have handy. Alcohol and drugs, legal or otherwise, should be avoided as they tend to increase the likelihood of accidents.
Tight bondage and hands-above-the-head positions tend to figure in many fainting incidents. Fainting or a fall can easily result in strangulation or dislocation and ropes can be pulled out of position or result in unexpected stresses. Watch out for any sudden rise in body temperature and clamminess as this is often a warning sign. In such incidences, slackening or removing ropes is usually a good idea, making sure you support the subject.
As fainting is the body's way of attempting to restore circulation, sitting with the head lowered or lying down with the legs elevated is beneficial. It has been suggested that loss of consciousness could occur from 'harness hang' syndrome. This is a condition common in rescue situations where the victim is held motionless and largely vertical by a harness. In such cases the normal treatment for fainting could be very dangerous, as circulation needs to be restored gradually to avoid a toxic shock reaction. Fortunately I've never heard of a confirmed case as a result of bondage, and as you shouldn't be doing suspensions yet it shouldn't be a problem.
When you tie someone, you remove not only their ability to prevent falling, but also their protective mechanisms. If you get jostled and feel you might lose your balance, the first thing you do is try to regain your balance with your arms. When you're tied, you can't do that. If that doesn't work, a leg goes out to stabilise you. Again, impossible if your legs are tied. Put the whole thing together with a pair of high heels, and you have a very unstable result; unless of course you keep a hold of them or rig a safety rope which I'll show you in a moment. I often see this scenario or somebody negotiating stairs with arms bound at public events; it's an accident waiting to happen.