Distillation will remove MOST contamination, but as posted above it WONT remove volatile hydrocarbon contaminants that have a boiling point similar to water.

Distillation followed by filtration through activated carbon should render the water safe.

It is worth noting that some organic contaminates are long term cumulative poisons, and might be less of a concern in a short term emergency.
A level that is considered unacceptable in a piped city water supply that people drink for a lifetime, might be acceptable in a short term emergency.

In case of TEOTWAWKI, production and use of most toxic materials would probably cease, so it would not be a long term problem.