What Clark said.
Some contact cleaners have an oil base. Get too much of it on the dial cord pulley and it will slip. Chances are there's a long side and short side of the cord relative to the tuning knob and it slips when you try to tune against the slack in the long side. Make sure the cord hasn't slipped off a guide or pulley and the spring in the tuning condenser pulley is stretched slightly... That would tell you it's holding tension.
Before you do anything, draw a picture or take a picture with your digital camera of how the cord was installed. If all looks good your options are to remove the dial cord and soak it in isopropyl alcohol until the oil floats out, or try cleaning it in place with Q-Tips or paper towels. If the tensioning spring is bottomed out due to cord stretch you'll need to remove one end of the cord and re-attach it with an extra loop or knot at the post. That way it's a little shorter and a little tighter. Also wouldn't hurt to (carefully) oil the tuning condenser and tuning knob shaft so they move as freely as possible.
The dial mechanism is a very simple machine that shouldn't be that hard to fix, just make sure you know how to put it back together..............