Originally Posted by aggiegrads

This. The lower headset race is most likely pitted. If the headset is as old as the bike, just replace the entire headset.

A poor man's option is to replace just the ball bearings and re-clock the crown race. This takes any dents that are aligned with the top race and orients them in a different direction. It will help, but only delays the inevitable. The best option is to replace the entire headset.

There are many specialized tools needed for this: headset cup removal tools, crown race remover, crown race setter, and headset press. You can make some of these tools (or do without the removal tools because the parts will not be reused) but you risk damage to the frame and/or fork if you are not skilled at using those tools. Other things can go wrong - the quill can be seized in the stem, the headset threads can be buggered, or the form may be too long or too short given the stack height of the new headset. Although this may be a costly problem, it is a good case for one of the few services that it pays a shop to perform rather than doing it on your own.