Indexed headset - repair or replace?

This normally happens if the headset is loose - when you go over a bump this makes the ball-bearings knock against the bearing races, which eventually hammers little depressions into it (the engineering term is brinelling, I think)

Here's a beautiful illustration of what you are describing... Tandem headset bottom race... The rest is not as bad, and the "brinelling" mainly happened to the front, I have re-installed it with the depressions to the back, it works a bit better until I have a chance to change the races/cups/bearings etc...