Of course the "Revolver check out" will be more complete, but. . .
Some quick checks one can perform (gun UNLOADED of course - must be checked by opening cylinder and making sure every chamber is empty, and I do this every time even when I think I left it unloaded since one's life is at stake):
1. Cock the hammer single action, pull the trigger while thumb is lightly engaged on hammer, and gently let the hammer down with thumb: make sure the cylinder cycles properly through all 6 chambers.
2. With the hammer cocked (cylinder in position to fire bullet), try to lightly rotate the cylinder side-to-side. No more than minimal play (perhaps 1 or 2 mm total) should be present, and the cylinder should tend to return to center. Make sure the cylinder locks positively into each of the 6 positions. That "Revolver check out" should contain a definition of full lock up, which I believe involves holding the trigger back after the hammer drops to check cylinder side-to-side movement, but I believe hammer cocked position tells you roughly where the cylinder will be at the instant the hammer drops to fire the round.
3. Roughly check that each chamber lines up with the barrel. There is a special gauge for this but I check it visually, sighting down the barrel with a bright light shining through the gap between cylinder and barrel.
4. Speaking of that barrel/cylinder gap, sight on it sideways with light behind and make sure it is little more than a sliver - ideal measurement is 0.006". Then grasp the frame and try moving the cylinder fowards and backwards relative to the frame - this end play should also be minimal.
5. Open the cylinder and sight down the barrel with a bright light illuminating the recoil plate. This should allow you to inspect the barrel bore for any obstructions or debris. I always clean this passage out with a standard gun-cleaning bore brush before firing.
6. With cylinder still open, inspect the breech end of the barrel and forcing cone for cracks and general condition. It should appear as normal machined metal with a barely visible conical inner profile.
7. Inspect each chamber in cylinder and OD of cylinder for cracks or other damage. There should be none.
8. Inspect the frame for cracks or deformation. Look closely at area just above barrel/cylinder gap as this is where flame cutting (erosion) from escaping gases may occur. Most used guns will have some erosion there, but it would have to be pretty severe to be dangerous.
I think that with these checks, one can be reasonably safe in test firing it. Others may disagree or have more to add. Naturally, the optimal thing is to take it to a gunsmith for full proper inspection. I am no expert, but just think of the obvious mechanical alignments a gun must have in order to pass a bullet properly. The pressures in a fired gun are astromonical (on the order of 10,000 - 30,000 psi) so it is nothing to trifle with. The model 66 is fairly robust, but any machine can be ruined by misuse. Good luck and hope this helps.