Chemically removing rust without leaving any unwanted residues
The common DIY rust remover is cola of some sort -- most colas contain a significant quantity of phosphoric acid, which reacts with the iron oxide to form iron (III) phosphate which you can then scrub off. Any remaining iron phosphate should come off with time and/or more water, and is harmless in domestic quantities.

(Wikipedia:Phosphoric acid - Rust Removal)