I was recently given several revolvers, Two of them spit lead shavings back at me when I fire. The revolvers are both S&W, one a blue 6 1/2 inch mod 29 44 mag and the other a SS 3 inch mod 60 357. Both seem very well cared for and show very little wear on the finish. What is the fix??

First, a THOROUGH cleaning.
The best way to clean a revolver, is to buy a Lewis Lead Remove kit from Brownell's.
This is an old stand-by tool used by just about ALL older revolver and pistol shooters.

The reason for the tool is, it completely removes all lead from the bore, AND the critical forcing cone at the rear.

There are other methods, but the Lewis is safe for the gun, and unlike other methods does clean the forcing cone properly.
Less than $15.00 from Brownell's.

When cleaning, use a brass "tooth brush" and a good gun solvent to scrub the face of the cylinder, and the face of the barrel around the forcing cone.  This is too remove all build up of fouling.

For the stainless steel gun ONLY, use a Lead-Away type cleaning cloth.  These are yellow cloths sold under various brand names that strip fouling off guns ASAP.
Use the cloth to clean the front of the cylinder and rear barrel.

DO NOT use on blued guns, it will strip the bluing RIGHT off.

Once it's CLEAN, check for end shake, (forward and back movement of the cylinder when closed), and use a set of feeler gages to check barrel/cylinder gap.  
It should run less than a MAX of .010, and better still around .005 to .008.

Closely inspect the all-important forcing cone for eroded or rounded off outer "edges", or any signs of alteration by "Bubba".
Check the front of each chamber for eroded and rounded "edges".

TRY A DIFFERENT BRAND/TYPE OF AMMO.

Test fire to check for spitting.  
Remember, ALL revolvers spit to some extent, and remember, one place people really complain about spitting revolvers is in INDOOR ranges.  
The alley barriers at each station often direct firing particles back to the shooter.  Shoot outside

If everything looks OK, and different ammo doesn't help, you may require a trip to the factory for repair.

In addition to the above a thing to check is cylinder lockup. When YOU have made sure that the gun is empty, pull the hammer back. Pull the trigger and hold it all the way back. How much play (rotational) is there? Do this for each chamber in both single and double action.

Use a dowel or visual check to make sure that the chambers actually are lined up properly for each chamber, again, in both single and double action.