"If I pull the trigger with the safety engaged, I hear a "click". What is this?"
"Sometimes when I have the safety on and press the trigger, the hammer moves forward a very small distance. What' s wrong?"
"Sometimes when I disengage the thumb safety, the hammer falls? What's happening?"
The answers to all three of these questions is the same. The sear is being allowed to move when the safety is engaged. Let's look at this in more detail.
When the trigger is pressed rearward to fire the Hi Power, the lifter moves up and engages the front end (with respect to the muzzle) of the sear lever. As the lifter pushes the lever upward in front, it rotates on a roll pin in the slide and the rear end presses down on the front of the spring-loaded sear. The rear end of the sear that engages the hammer's full-cock notch moves upward and when it clears the notch, the hammer drops and the pistol fires.
When the safety is pushed upward to engage and make the firearm "safe," it blocks the downward movement of the front end of the sear should the trigger be pressed.
If the little nub on the thumb safety that butts up against the sear is just a little short, the sear is allowed to move downward by that amount. If this is miniscule, you will sometimes hear a faint "click." The hammer has moved, but is usually not enough to really be seen even if looking at it. This is usually the case, but not always. It depends on the hammer/sear interface as to whether or not any sound is heard.
If the hammer moves with the safety engaged and the trigger's being pressed, the very same thing's happening, just to a greater degree.
If the hammer falls (hopefully to half-cock), the sear is being allowed to move enough to allow the sear to completely disengage the full-cock notch when the safety no longer blocks the rest of the sear's downward movement. How much will allow this depends on a number of things including the angle of the sear face and how closely it mates up with the full-cock notch in the hammer.
The fix is simple and not expensive. A gunsmith can build up the short portion of the thumb safety that protrudes to block the sear movement. He will then dress it down for an exact fit where no movement is allowed should the trigger be pulled. Unfortunately, this fit must be exact or nearly exact to prevent this problem and the factory does seem to "miss" now and then. Cylinder & Slide sears come oversized and require fitting so that the fit can be done exactly right for the particular pistol.
It's normal to want to check your Hi Power for such safety issues. If you do this, be sure the Hi Power's not loaded and don't pull on the trigger as hard as you can or until you get white knuckles. Just give a firm pull. If there's a problem, you'll see it. If not and this action's repeated time and time again or done with as much force as can be mustered, it can create the very problem that was being checked. I have found the factory sears to be more prone to this than the C&S, but again, the fix is easy and usually long-lasting in my experience.