I've noticed a significant "popping" sound from the right sidepipe when I down-shift or release the gas and slowing down in gear.

Just had a new distributer, carb, wires, plugs, etc. installed.

Any ideas as to what's going on?

I have about 94K on the engine (L-48) all original. Car is a 76.

I had what sounds like the same issue. In my case the popping was a sharp snapping noise and it only happened when down shifting or lift my foot off the gas pedal. I have a 4.11 rear so lifting my foot off the gas pedal is like down shifting.

The issue was water in the gas. I looked in my gas tank with a flash light and I could see that there were two liquids in there. At the time I had less than 1/4 tank of gas. I drained the tank, threw in a can of dry gas and a filled it up. That resolved my issue. Right, wrong or indifferent I did not drain the carbs. I have tri-power setup that doesn't leak and currently works well. So I chose to let the engine deal with whatever was in the bowls.

I was warned that the water could return from condensation if I don't keep the tank full. Currently I drive my car a lot so that's not a problem. I believe that my issue was from a bad fillup. I got gas at a station I had never been to before and right after that the noise showed up.

It could be water in the gas, I guess it depends on what kind of popping it is. I had an exhaust type of pop on the right side and it was caused by a leak where the header attaches to the pipe. After I closed it up the popping went away.

If your engine wasn't popping before you had your Carb and distributor work done, I would start my search there. Recheck all the simple stuff, timing, plug wires in the proper place on the distributor. Wires have even been known to leak voltage when they are new. Good luck.

Check your header gasket on that side and make sure all your new wires are firmly connected. Since it is only one one side, I think you can forget about the carb or timing.
I just went through the whole gambit you are in now. I found a loose rocket arm and a bad seal on the header gasket, both on the same cylinder.