Here is the Comparison of Water Treatment Methods in that book on page 156.

Steam distillation removes the following:
Alluminum
Arsenic
Bacteria
Benzene
Bromide
Cadmium
Calcium
Chlorides
Chlorine
Chromium
Cryptosporidium
Detergens
FLUORIDES
Herbicides
Lead
Magnesium
MERCURY
MTBE
Nitrate
Organics
Pesticides
Phosphates
Radon
Sediment
Sodium
Sulfates
Sulfide
TDS
TTHM
Viruses

Reverse Osmosis removes the above except for:
all of Arsenic
all of Bacteria
all of Nitrate
Viruses

The question whether it removes Fluorides is debated right now.

For comparison sediment filter does not remove anything but

Sediments

And Carbon filter only removes

Chlorides
Chlrorine
some Chromium
some Detergents
Herbicides
MTBE
Organics
Pesticides
some Sediment
some Sulfates
some Sulfide