This is from another site, but seems to be the cure.
Clean the two small brass tuning wheels behind the front panel. You can use Deoxit, rubbing alcohol or the cleaning agent/solvent of your choice. A Q-tip is helpful. Concentrate on the areas where those two wheels mate. Make sure the surfaces are super clean. Even if they look clean, they may still have dirt on them. Examine them with a magnifying glass to check for any dirt that you missed. Make sure you clean the groove on the top wheel. Clean these wheels until a clean Q tip no longer picks up any dirt. Most of the time, that will solve your slippage.
You can also buy rosin from a music store. Apply it to the mating surfaces of the two wheels. It will add some traction, at least for a while.
Don't mess with that S spring unless absolutely necessary. It is a pain to remove and an even greater pain to re-install. It tends to shoot across the room and hide in the damnedest places. If you lose it, you're screwed.
If you're going to lubricate the gears, make sure you position the chassis so the lubricant doesn't hit the two drive wheels. A stray drop of lubricant can, by itself, cause dial slippage. In fact, a prior owner's careless use of lubricant could be the cause of your current slippage.
Here is the site that Warren referred to: http://www.radioblvd.com/sp600_rebuild.htm It's an unbelievably good resource for the restoration of SP-600s.
I hope this helps.
Joe Connor