Likely not all of the impurities. Those with boiling temperature similar to water will probably mostly remain (it's more complex than that). A better question

Likely not all of the impurities. Those with boiling temperature similar to water will probably mostly remain (it's more complex than that). A better question would be: Are there dangerous levels of contaminants in after a single distillation pass? For municipal water - probably not. For chemical factory effluent - probably yes. Plastic pipes after wildfires - no idea. Also, you need to add something to distilled water, as it's shocking to a body. Almost anything will do, though you may need to think about mineral content in the longer term.