http://www.wellness-water-filter.com/dis_rev.html
Distilled vs. Reverse Osmosis
The two most commonly recommended types of water by doctors are distilled water and reverse osmosis water. Both types are generally very pure although both can allow the carry over of trace contaminants if boiling points are similar or if molecular size is similar. Unfortunately, many advocates are unaware that ultra pure water is not the best for regular long-term consumption and that it can carry an unexpected long-term health risk.
Distilled water is boiled and evaporated. It has no minerals in it and the very structure of the cell of each water molecule is also stripped away; depending upon how it is treated, it may contain chemicals like nickel and aluminum. In my opinion it is not fit for human consumption.
To understand the reason why the purest is not always the best, one has to look at the basic chemistry of water itself. Water has what some chemists call a stability index. This index indicates how stable water is in relation to the chemicals and minerals in its immediate environment. Water naturally seeks to achieve a zero or neutral index. If water has a positive index at a given temperature, it will tend to release or precipitate minerals that are dissolved in it. One can witness the results of water having a strongly positive stability index (for example hard water) when such water deposits scale in pipes or hot water heaters.
Water that is on the negative side of the index is aggressive and prone to dissolving minerals and metals from its immediate environment. One can see evidence of such water when it corrodes pipes or produces rust. The more negative the index, the more aggressive the water is. Water produced from distillation and reverse osmosis has an extremely negative stability index. This water also actively absorbs carbon dioxide from the air and makes the water more acidic. When one drinks small quantities of this water for short periods of time, it has the special property of being able to absorb toxic substances in the body and remove them. This detoxification can be good for the body and can aid it in recovering from long-term exposure to certain contaminants. However, regular and long-term consumption of ultra-pure, demineralized water will also strip the body of magnesium, calcium and trace minerals. The more the mineral loss, the greater the risk of osteoporosis, osteo-arthritis, hypothyroidism, coronary artery disease, high blood pressure and a long list of degenerative diseases generally associated with premature aging.
The longer a person drinks demineralized water, the more likely the development of mineral deficiencies and an acid state in the body. A number of physicians, nutritionists and researchers now believe that aging and disease are the direct result of these deficiencies and lead to the development of an acid state in the body.
Dr. Zoltan P. Rona, a Canadian physician and clinical nutritionist, reports that exclusive consumption of de-mineralized water will, over time, lead to multiple mineral deficiencies. His research with over 3000 patients indicates that those who supplemented their purified water intake with trace minerals were not as deficient but still not as adequately nourished in minerals as their non-purified water drinking counterparts even after several years of mineral supplementation.
Put simply, distilled water and reverse osmosis water acts like a vacuum and will suck out many of the beneficial trace minerals you need to stay healthy. Obtaining good mineral balance is hard enough; one clearly does not want to put a metabolic drain in their system by drinking distilled water.
Fasting while using distilled water can be particularly dangerous because of the rapid loss of electrolytes (sodium, potassium, chloride) and trace minerals like magnesium, deficiencies of which can cause heart beat irregularities and high blood pressure.
Cooking foods in distilled water pulls the minerals out of them and lowers their nutrient value.
Another point involves alkalinity and acidity. Natural health writers generally agree that the body maintains best health when it maintains a ph leaning to the alkaline side rather than the acidic side, and yet distilled water quickly turns highly acidic, about 5.8 in an open air container.
Distilled water and reverse osmosis water is often sold as bottled water and a major worry with bottled water is the environmental concerns it creates. Bottled water is usually no safer, or healthier than tap water in many countries, yet it sells for up to 1000 times the price. As well, it is the fastest growing drinks industry in the world and is estimated to be worth US $22 billion annually.
Studies reveal that the bottled water market is partly fueled by concerns over the safety of municipal water and by the marketing of many brands that portray them as being drawn from pristine sources and as being healthier than tap water. However, some bottled waters only differ from tap water in the fact that they are distributed in bottles rather than through pipes. In fact there are more standards regulating tap water in Europe and the US than those applied to the bottled water industry. These studies also find that every year 1.5 million tons of plastic are used to bottle water.
Toxic chemicals can be released into the environment during the manufacture and disposal of the bottles. Furthermore, a quarter of the 89 billion liters of water bottled worldwide annually are consumed outside their country of origin. Emissions of the green house gas carbon dioxide, caused by transporting bottled water within and between countries, contribute to the global problem of climate change.
I don't have to do shit. That's my tap water I was talking about. Pay attention and leave the classroom behind. 
