If you rely on a double action revolver something that's easily overlooked is whether the thumbpiece nut or screw is tight. If it loosens and falls off it could lead to losing the thumb piece, thus making the gun a lot harder to load and unload.
The thumb piece nut is part number 20 in this diagram of the Smith & Wesson Model 10, with the thumb piece itself being number 21.
Taurus revolvers use a similar design. At least on the two sample I own an actual screw is used, that screws into the cylinder latch. On the S&Ws there's a threaded stud that protrudes through the frame onto which the nut threads.
I recommend removing the nut or screw, cleaning the threads with rubbing alcohol, and then reinstalling after putting some blue Loctite on the threads.
It wouldn't be a bad idea to pick up a couple extras along with other spare parts. Something else I recommend for older Smith & Wessons is a spare hammer nose and rivet (parts 48 and 51 in the diagram). Numrich is a great source for a vast amount of gun parts.
When working on guns always make sure that you use properly fitting, hollow ground screwdrivers. I mostly use the screwdriver bits found in this set from Weaver, which includes a good mallet, pin punches, and bench block, all of which are very useful.