Not really any. Bottled water is watched to make sure there aren't any obvious contaminants (lead, bacteria, etc) but not really to make sure it's pure or that there aren't trace minerals, sediment, or even the contents are what they say they are. It's not a drug, and as such is subject to standards for foods, such as a certain number of bug parts are ok, etc. Bottled water is not much cleaner truthfully than tap.
FDA regulated. http://www.fda.gov/food/resourcesforyou/consumers/ucm046894.htm is an fda website discussing regulations. You can get as good or better water with a little brita or pur filter and using your own bpa free container.