Safe water means water that will not harm you if you come in contact with it. The most common use of this term applies to drinking water, but it could also apply to water for swimming or other uses. To be safe, the water must have sufficiently low concentrations of harmful contaminants to avoid sickening people who use it. The list of harmful contaminants includes disease-causing microbes such as bacteria, viruses, and protozoans; cancer-causing chemicals such as many pesticides, organic solvents, petroleum products, chlorinated byproducts of the disinfection process, and some metals and metalloids; nitrates and nutrients, endocrine-disrupting compounds, strong acids, strong bases, radionuclides, and any other acutely toxic substance.
How do you define "safe levels"? The U.S. Environmental Protection Agency (EPA) sets Maximum Contaminant Levels (MCLs) for many harmful contaminants, based on health-effects research, contaminant occurrence data, economic analysis, and risk analysis. The MCLs for currently regulated drinking-water contaminants are listed on EPA's Office of Ground Water and Drinking Water Web page under "Drinking water standards program."
Keep this in mind: water that is safe for one person may be unsafe for another. If your immune system is weakened by HIV/AIDS, or by a recent bone-marrow transplant, or if you are a young child or an elderly person, or pregnant or a nursing mother, you are more susceptible to contaminants in drinking water than the rest of the population. Your doctor may urge you to take extra precautions with the safety of your drinking water. An online reference is EPA/CDC's guidance for people with severely weakened immune systems.
What are the permissible levels of trace elements (such as arsenic, copper, iron, lead, and zinc) in water for the water to still be considered safe?
Several of these trace elements are regulated by the EPA and are on their list of primary drinking water standards. These include arsenic, copper, and lead, as well as cadmium, chromium, mercury, and selenium. Iron is not a regulated contaminant because it is not known to cause health problems, but there is a secondary drinking water standard based on its tendency to stain laundry and plumbing fixtures. Manganese, copper (again), silver, and zinc are also included in the secondary standards. The primary and secondary standards are available on the EPA Web page Current Drinking Water Standards.
The above standards are national drinking water standards. Other water-quality standards are set by states to protect aquatic life. You can check with your state environmental or natural resources agency to see what aquatic life water-quality standards are in effect in your state. EPA is currently reviewing its recommendations for aquatic life criteria. Information on the current review of standards is available on Aquatic Life Water Quality Criteria.
The USGS National Analysis of Trace Elements also has current information on trace elements across the United States, including links to specific studies and current items in the news.