HOKAY DOKAY. I did some things:
First, I unscrewed the headlight and tried to open it up. Tried, and failed... it would come out half an inch and catch. Took me a bit of messing around to get into it, and when I did I discovered the problem was those screws that allow the sealed beam (as 5twins mentions) to swivel when you adjust it side to side.
See, the large rubber washer thing and the metal washer were on the outside, and there were no nuts on the inside. Seriously. I had to go back and review the fiche to make sure I understood how it was supposed to go together. As I was marveling at how screwed up it was, I found the missing nuts (and those two little bushings)... lying in the bottom of the headlight bucket, trying to fall out on the floor.
I brought all the bits into my office (where I normally service computers), laid it out on my workbench and took it the rest of the way apart. The rubber ring that goes around the sealed beam? Not lined up with the bumps. Nor were the bumps lined up with the reliefs in the metal ring where they were supposed to be.
So I carefully put it all back together as indicated in the parts fiche, and it looks a lot better now.
Then I turned my attention to the turn signals. Here is the right signal, before:
And after:
And the left, before:
And after:
I fixed the warped baseplates (whatever those are called) by putting them in a vise with a flat, smooth piece of cheap metal pressed against the top side to protect the finish. The studs got fixed by the same means as the left rear... I threaded three 13mm nuts onto the studs to protect the thread, then slipped the assembly into an iron pipe and bent it straight. That last one, the left front, had to be readjusted several times because it was bent in two distinct places, and it's not perfect but I don't think it shows too much.
Finally, I turned my attention to the faulty blinkers. The right blinkers started working again, mysteriously, but no left blinkers. I rearranged the connections in the headlight so that it would activate the left blinkers if I signaled right, and lo and behold, they worked. Thus, it had to be the switch. I started disassembling the pod and discovered that yes, there is a bad solder joint... two, in fact, one on the left turn side and one on the common connection. The common connection must have been cutting in and out, which explains the intermittent failure of the right turn signals.
I also found this:
Note the loose connection hanging there. I'm not sure what it is. I've accounted for both signal wires, and all the other lights and indicators work (or at least, they did before I took the left pod apart) so I don't have a clue where it is supposed to go. Anyone have a clue to give me?