So first the questions:
1) What sort of interior cabinet corners do the current Sterns have? Mine has these heavily reinforced leg-bolt holders. Are these standard, or were they added after the fact?

Yes I think this is now the standard. A few games ago they were having issues with splitting cabinets so I'm glad they are back to this practice.

2) Why do the leg bolts have washers on them? None of my other pins have had washers on the leg bolts. Are they necessary?

It is obviously your preference if you want to use them. I thought it was odd that Stranger Things had them so it must be standard to avoid scratching/chipping.

3) I moved the inlane posts to their narrowest position (None of us are great players yet). For the right-hand post, after unscrewing the nylon nut from the bottom, I had to manually loosen the post by hand to remove it. The post was so tight that I had to use a pliers and loosen it, and it tooks ages to loosen and re-tighten in it's new position. It went even slower because I had to be really careful not to bump the plastics or playfield, so it was quarter-turn by quarter-turn. Is there a better way to loosen/remove these types of pf posts? Is there a special tool? Or is a pliers and patience all we've got.

Yeah a deep socket is your friend here. I moved the posts on Stranger Things and had the same battle until I moved the ramp and used a socket. The hole in the wood is tight and you will have to tread them in and out.

Next, the observations:
1) This pin is A LOT lighter than my other games. I actually consider this a good thing because it's much easier to transport and move around within my house.

Yup. The older games were built like tanks. You can definitely notice when you nudge them.

2) The cabinet and head seem much more fragile than my old Williams games. It seems like it takes almost nothing at all to chip away at the edges of either. It seems like it would be a lot easier to damage this cab than the old Williams cabs.

Sad but true.

3) The pf mounting system seems cheaper and more clunky than my WPC games. Once I've fully raised the PF vertically, it's a bit of a pain to get it to slide all the way back after I've lowered it back down.

Sad but true. The locking system the older games had that keep you from sliding the games off the rail is missed.

4) The flippers feel really good, and I like that Stern is still using leaf-switches. Makes it much easier to fine-tune and adjust the flipper buttons to my liking than with opto-flippers.

Agreed!

5) Are the power-supply fans really this loud on all current Sterns? It's ridiculous. I've ordered Pinball Monk's quiet fan and will be installing soon.

Sad but true. I did one of Monk's replacement fans in my TNA and it made a huge difference. I will be buying one for TMNT.