Tap water can be a pain as it will possibly contain high levels of nitrate, phosphate, silicates and organics, all good ways tp give you difficult to fix algae problems.
Rust is overrated as a problem. Chlorine is a non starter as you stuff the water full of Cl- ions anyway.
Heavy metals may or may not be a problem - you can scout around for research by Richard Harkerwho has evidence the biological activity elevates heavy metal concentrations round reefs far above NSW levels anyway, in contradiction Dr Ron Shimek reckons they're satans work, and others reckon it jsut doesn't matter.
You might bear in mind your tap water is not my tap water - my tap water sometimes has lower TDS than some peoples RO - if you live in a large metro area or live in a country which has flaky water standards (much of the US) then don't use tap. Lets just say RO units don't sell well in Scandinavia.
FWIW well water is very likely worse!