He's not worried about removing the rust, but what to do to prevent it from coming back. First a little background on removing rust.

While oxalic acid dissolves rust (actually converts it into a water-soluble chelate), it also dissolves bare metal at an equally fast rate. It will also creep across underneath the chrome-plating and remove the good metal underneath, causing the chrome to flake off easier. A much, much better compound to use is Naval Jelly (phosphoric acid). The reaction is similar in forming oxalates, but phosphoric acid eats away bare metal MUCH, MUCH slower than rust. It also leaves a thin coating of iron phosphate on the surface, which protects against further rust & damage (only temporary). With either compound, be careful with the handling as the oxalates formed are reactive with the iron in your blood just like cyanide.

For the OP, he can just touch up the spots that had rust removed with grey-primer. Use a small brush or Q-tip to apply. It blends in fairly well with chrome finish. And on old bikes, it's much, much less noticeable than rust.