PG is apparently not altered by heat and has a very long history of safe use for inhalation, though not in the high quantities that vapers inhale - and not both heated and in high quantities. For example it has been used for aerosol dispersion in hospitals to reduce infection. Despite favorable results[1] this has apparently not been widely taken up.
VG has little history for this purpose and when exposed to intense heat can produce a poison, acrolein. Tests[2] have shown that no acrolein is produced at the common
vaping temperatures. Otherwise, it appears to have little implications for inhalation but without controlled long-term testing, nothing concrete is known. Both PG and VG (which are chemically very similar) are broken down by the body into simple carbohydrates.
PG and VG are both deemed safe for inhalation but this does not mean they cannot harm somebody somewhere. Intolerance to one or the other is not uncommon, and in this case the other type should be tried. VG can be made in several different ways and only the 'Glycerin, USP' product should be used (it can be made from coconut oil and/or palm oil, or as a byproduct of biodiesel manufacture). There are a small number of people who may be allergic to coconut oil and therefore need to try a different brand of VG or move to PG or PEG.
PEG (polyethylene glycol) is the third, and least-used, carrier liquid. It is thought to have some advantages in taste, and is reported as the least problematic for those persons who have a wide range of allergies and intolerances.
Nicotine is not altered by heat and has little health implication except for specific groups of persons such as those with heart disease. Otherwise it might be considered in the same class as caffeine. It is measurable in the blood of the whole population since it is present in significant quantities in the food chain (both as a natural plant ingredient, and possibly as an ingredient in insecticides applied to vegetables); and in one form it is a vitamin needed for full health (vitamin B3, aka niacin or nicotinic acid or the synthetic version nicotaminide).
The carrier liquids, and nicotine, are not thought to have great potential for harm. Flavors are another matter. Most flavors are based on food flavoring, which has no history at all for inhalation. In fact we know that some chemicals known to be present in food flavoring and that therefore appear in e-liquid should not be inhaled, diacetyl[3] being a classic example, since as a food additive it is harmless but when inhaled in quantity[4] it can cause an incurable lung disease.
Some flavors such as plant oils have been used for inhalation safely. Other flavors may be entirely harmless, or there may be health implications - there is absolutely no way of knowing. The safe option is to use as little as possible; but a conflicting opinion is that since e-cigarette use is likely to to be 1,000 times or more safer than smoking tobacco, there is not much point in worrying. Nevertheless, if any form of reaction is experienced to e-liquid then the first thing to do is remove/reduce/change the flavorings, as these (and any 'unlisted' additives) have the most potential for harm.
Or if you prefer a statistical analysis: 450,000 a year are said to die in the US as a result of around 17 to 20% (estimates vary) of the population smoking. When smoking, more than 4,000 chemicals are inhaled, many of which are known to be toxic or carcinogenic. Vaping involves the inhalation of between around 5 to 20 chemicals, depending on the e-liquid in use.
However, despite the massive reduction in the inhaled materials, it would not just be extremely optimistic but highly improbable that zero deaths would result if all smokers converted to ecigs. We have to allow for some deaths due to individual susceptibilities in some persons, or unknown factors in ecig ingredients. That number is naturally a subject of hot debate but for the sake of argument let's call it 1% or 4,500 deaths a year. Too high? OK, let's call it 0.1% then - 450 deaths. You're an incurable optimist? OK then, 0.01% and 45 deaths a year.
So if we, temporarily, agree that vaping potentially has just a fraction of the death rate of smoking if all smokers converted to ecigs, then you must also agree that those deaths would be caused by something. The 'something' has to be an either individual intolerance to an ingredient in the liquid, whether it's a flavor, hot PG or even just the nicotine, or disease caused by factors as yet unknown to us.
Therefore no matter how 'harmless' vaping is, it will kill somebody somewhere. If you, personally, want to reduce any possible risk even further, then no doubt some options have suggested themselves during the reading of this (highly speculative) answer.
Notes
[1] There have been several trials of this. Some childrens' hospitals apparently ran long tests of 3 years plus in the 1940's. In one hospital, taking a one-year period, with two wards studied, it was reported that there were 95 infections in the control ward (no PG aerosol) but just 5 infections in the PG-treated ward. The infections prevented were of several types including the common cold.
[2] Intellig's tests at 300 degrees C showed none, their standard atomizer runs at 280 C. It might however be expected that high-voltage mods could exceed this, although acrolein reportedly has a strong unpleasant aroma.
[3] This is the synthetically-produced active ingredient in butter/popcorn smell. It is present naturally in many foods, but the issues are with the highly-concentrated synthetic version, which is used in microwave popcorn and some buttery-flavor e-liquids.
[4] Nobody knows exactly how to define 'quantity' for this purpose - the amounts in vapor may or may not be significant.