Joe,
Thanks for the video. It did help me understand how things go together. Took the right side safety out, cleaned a little, and put it back in. It seems to be functioning about the same (same slop), but a little more crisp. It looks like the detent was seated properly before. As far as I can tell, the safety is still functioning fine. The sear does not move when I have the safety on while pulling the trigger.
Perhaps this is just my lack of memory for how it was exactly before I started moving things. I did some light tapping with the slide in the frame that may have shifted the safeties (while centering the firing pin retaining pin). After taking the right side safety out, I don't see how I would have damaged anything. It looks like there are other threads with concern about slightly sloppy ambidextrous safeties that appear to not affect the general operation of the thumb safety.
A few more observations. I'm right handed. I use the left-side safety with my thumb. If I just use that side (push it up all the way), the right side will come most of the way (to the lower position in the above post). I was observing what happens if I tried to pull the trigger like that - and noticed the right side safety moves up to the higher position (detent fully engaged) when I do so. Interesting, but still nothing that I would consider hazardous. If I use the right side safety (i.e. left hand), then the left-side safety goes up all the way. It's a little more crisp of an engagement, since both detents are fully engaged.
Nate