There can be a number of reasons this is happening. The simple way to find out is to have a good S&W gunsmith take a look at the gun.
Is it always the same chamber(s) that cause the problem? Try loading every other chamber (odd numbers) and firing. If okay, repeat with even numbered chambers loaded (you decide odd/even).
Things you can check are;
1. Check ammo for high primers - especially on reloads. Inspect after gun jams to see if you have any horizontal marks on the primers.
2. Check ammo for improper bullet crimp. If firing reloads especially. When the gun jams keep weapon downrange and level, finger OFF the trigger. Lean over to right and check the next chamber to cycle up (on the right of the gun). Do you see a bullet nose peeking out and contacting the forcing cone of the barrel? How about at the bottom near the left side of the frame/cylinder yoke? Your M65, with .38's should have what looks like 1/4" depth between bullet nose and cylinder front.
3. Ejector rod unscrewing. Open cylinder and check by holding cylinder and trying to unscrew the ejector rod either direction. If it unscrews in the locked position you may not be able to open the action. If this happens you may need to use padded needle nose pliers to carefully screw down the ejector rod to get the action open. After that, unthread the rod, degrease the threads and put some fingernail polish on the threads before reassembling. Note: Threads may be a left-handed (reversed) thread!
4. Check the recoil plate for gouges or machine marks. The recoil plate is the raised portion of the frame behind the cylinder that keeps the cartridges from falling back out (just ahead of the cylinder release). Occasionally a gouge or machine mark will cause the edge of a cartridge to catch. Inspect for any area showing "gold" (brass) smears or particles. Can be smoothed with a soft Arkansas stone and light pressure.
5. Weak extractor rod centering pin spring. The spring that pushes the pin out at the center of the star extractor. If the spring is weak it can allow the cylinder latch to ride forward and jam the action. It can also allow the shooter to jam the action with slight forward pressure on the cylinder release. Likewise a weak cylinder release spring keeps the latch forward instead of rearward.
6. The internal hammer block binds on accumulated gunk or has slipped out of its slot in the sideplate. Clean the action with the hammer back using a spray degreaser and relubricate.
Barring any of these issues, visit your local gunsmith.
