The problems with bottled water start with the bottle. Even if the water were as pure as possible when it was put inside, the bottle itself is a wonderful product of modern chemical manufacturing. Why plastic in the first place? It's cheaper and lighter in weight than glass. Lighter weight means lower shipping costs. The plastic is Polyethylene terephthalate (PET). This is the same plastic used in carpet fibers and in polyester clothing. Of course, for use in bottles, it isn't dyed.
The fact that water bottles have to be clear plastic - because that is what consumers prefer - is a problem of another sort. Recycled plastics usually have small amounts of dyes from their previous life. That means, to make a clear plastic water bottle, you have to start with new plastic. Cleaning recycled plastic to an acceptable level is cost prohibitive. So every bottle you grab started out as oil extracted from the ground.
While starting with pure PET keeps the bottle looking good, it doesn't solve other problems. Plastics contain other chemicals used to alter their properties - changing the stiffness or keeping them resistant to breakdown from light. For PET water bottles, chemical additives can leach into the water. Other contaminants end up in the plastic as a result of the high temperatures used to melt and shape the bottles.
Two Main Contaminants
Antimony is a heavy metal used as a catalyst in PET plastics - including water bottles. It is used as Antimony Trioxide in small amounts to help the plastic form the proper cross-links. The disturbing thing is that the metal ends up in the final product. Migration is the technical term for movement of chemicals from the container to the foodstuff inside. It happens with many products, and it happens with PET plastics and bottled water. Manufacturers do test to see how much ends up in the water, but there is no clear 'safe level'.
Another contaminant, acetaldehyde comes from the manufacturing process. Manufacturers are aware of this one too. In the case of acetaldehyde though, it the concern isn't so much about poisoning, it's about taste. Humans can taste acetaldehyde at concentrations as low as 10 parts per billion. It has a disagreeable taste and odor. In other products, this defect is hidden by the taste of the product - a little sugar or artificial flavoring can hide it. But this doesn't work with water. You can't convince people they are drinking clean, safe, healthy water if it reeks of a chemical plant.
Acetaldehyde isn't added to the plastic on purpose, it comes from degradation of the PET during manufacturing. Overheating or over-stretching the plastic when it is shaped into a bottle creates this contaminant. Properly adjusting machinery will reduce it, but some will always form. If you've ever seen a white, cloudy patch in otherwise clear PET, it is likely a result of acetaldehyde and problems with the extrusion machinery.
Other Costs of Bottled Water
Disposal of PET water bottles is an issue. Only about 25% of the bottles ever get into the recycling stream. Most end up in landfills. Since approximately 50 billion water bottles are purchased in the United States every year, the numbers mount up. Transportation is another cost, both in economic terms and because of the associated pollution. Tap water is transported a relatively short distance through pipes. Bottled water, on the other hand, is packaged individually and in case and pallet lots, then stored, then shipped (sometimes thousands of miles from the bottling location), then refrigerated, then bagged up and transported home by the consumer.
The final result of all the movement, fuss, and costs is a thirsty person with a bottle of water... a person who is probably within a yard or two from something just as good (or bad!) - tap water. From a cost benefit point of view, the whole idea is insane. We add to the price of an everyday item strictly for style reasons. All the fuss and bother results in a much higher price for something you've probably already paid for that takes less effort to get - turning a tap instead of unscrewing a top.
In the end, the biggest problem with bottled water might be the label - a label so attractive that we willingly spend a hundred times what we should for something we already have.