I have a Marlin 336C (circa 1973) in .35 Remington that has suddenly started misfiring a lot.

Then a friend of mine says that Marlin had a problem with this gun in this caliber seperating head space. Said his went back to Marlin for repair years ago.

Anybody ever heard of this problem?

I've seen several, all 35 Remington that have had the same problem. Yours may or may not be a headspace problem. A new locking bolt should cure it. The locking bolt on a Marlin locks the bolt into battery and pushes the two piece firing pin up to allow it to fire. They are not a drop in part and have to be fitted.

If Marlin will fix it, that's the way to go.

Headspace problems don't suddenly occur with the 336 unless the barrel is loose or the locking bolt is soft. I would inspect the 2 piece firing pin assembly first to make sure something wasn't interfering with the alignment of the two pieces. You can check this by closing the bolt on an empty chamber and then press the firing pin forward. You should not feel any interference with the forward movement of the pin. If you do, then that is where I would focus my attention first.