The panel is just vinyl wrapped cardboard so its important to pry on the clip so you don't tear the backing.
Here you can see lever pulls on the metal clip and not the panel. Once the panel was off i vacuumed the bottom of each door to remove any crud. Any loose dirt and grime in the bottom of the door will hold moisture anytime water gets inside the door, making it easier for rust to form. There was some loose sound-deadening material that had flaked off the inside of the door and had stuck to the bottom. One piece had even managed to seal one the drain holes closed.
Here's why the passenger side cylinder was loose. The metal retaining clip that holds it in place had fallen off. Simple fix. But when I tried the key in the cylinder it wouldn't turn. It doesn't feel like all the pins inside the cylinder are contacting the key. I don't know if the cylinder on that side is even keyed the same, or it's just dirty inside, or even worn out. For now I just put everything back--at least you couldn't open the door just by turning the cylinder anymore. While I was in there I saw that the rod going from the outside door handle to the latch was bent. This didn't look right so I straightened it out somewhat. However, I neglected to check whether the door would open from the outside. Sure enough, after I buttoned everything back up, the door wouldn't open from the outside. Well, maybe next time.
The driver's side lock mechanism was way stiffer than the passenger side. I'm guessing the parts are more worn out since they've probably seen a lot more use. I lubed up the linkage the best I could and it started working better.
Here's the driver's side cylinder. You can see the clip is in place but is not slid far enough to the left where it would lock into place. This allows the whole cylinder to rotate, leaving that circular wear pattern on the door. When the clip is slid all the way to the left it contacts the edge of the door and prevents the cylinder from spinning. Another simple fix. The key now works the lock but it can be finicky. It's probably pretty worn. At least now I can lock up the car, but I can only open it from the driver's side. A new door lock and ignition set is only $30 so I may have to invest in one. It would really suck if I couldn't get back into the car because the single lock finally wore out.
Ok. I splurged on a new lock set. I even paid extra to get the Pony key. I replaced the passenger side lock first since it had other issues from my previous attempt. I figured I'd tackle the non-operable door handle first. As soon as I removed the door panel the problem was obvious.
The operating rod on the left is supposed to be snapped into the black plastic bushing in the center. It must've popped free when I was straightening the rod. Here's what it looks like in place.
I pulled the old cylinder out and it was clear why it wasn't working--most of the pins were missing.
The old cylinder on the left is missing the cover that keeps the pins and springs in place. With the new cylinder in place the lock worked as intended, although stiffly. Someday I'll pulled the latch assembly and see if I can clean and lube the mechanism.
I also replaced my front seat belts. The old ones were rusty and didn't adjust very well.
UPDATE: July 2017
I finally did get around to removing the driver's side door latch. I needed to replace the window regulators since it took two hands to raise the windows, so I figured it was a good time to lube up the latch. They are not easy to get out and put back in but I did it. It was especially frustrating getting all the operating rods back in place and functioning correctly. I ended up replacing the driver side inside door handle mechanism since the spring was broken. I also found these cool washers to fix the stripped out latch mounting screws.