Are you using the RF out into your TV, or the composite video output?
It may just be a problem with the RF modulator.
Or it could be a problem with noise on the 5V power supply line, which may suggest dried out electrolytic capacitors in the ripple filter. If you have an oscilloscope handy you can see how much noise on is on the power supply lines.
The C64 contains lots of socketed ICs which can become intermittent over time. Just like in many Amigas.
Remove and reseat all the socketed devices inside.
