I had this almost done, when I clicked on one of the bookmarks on my toolbar instead of another tab, and discovered that Dreamwidth apparently doesn't save drafts like Livejournal does. Darn it.
The dream was entirely Firefly, but it wasn't like I was watching an episode, which has happened sometimes. It kept switching viewpoints- first I'd be one character, then it would go to third person omniscient, then back to another character- it was confusing. The "episode" was set on this swamp planet, where all the buildings were several stories in the air on wooden stilts, connected by wooden walkways, for some reason- either things close to the ground rotted too fast, or the floods were too frequent, or the ground was so swampy that they just sunk. There were large carnivorous dinosaur-esque reptiles on the ground, but that wasn't the reason. Also, it rained all the time on this planet, and throughout the action of this dream there was a constant drizzle, which was apparently as dry as it ever gets.
The first bit I remember is Inara as the viewpoint character, on one of these walkway-sidewalks. Someone ran past her and pushed a baby into her arms, and instead of chasing them, she went in the direction they had run from to find two other women with babies of different ages, which held their heads up and looked at her. Nothing else happened with this plot ever again.
It then switched to Simon's viewpoint. He, River, Zoe, and Book were on a similar, nearby walkway after a heist, which had, unsurprisingly, gone somewhat south. There was some ship or shuttle (not Serenity) that was supposed to meet them on that walkway, but it wasn't there and the local police were on their tail. There was a narrow wooden emergency ladder leading down to the "shore" (it was marshy enough you could barely tell), where there was an old wooden rowboat, but there was a dirty bowl (identical to the ones from Cool Dining Hall, oddly enough) wedged in the top rung, which, by dream-logic, made it impassable. After a bit of arguing, Simon leaned over the railing and knocked the bowl out, but no one wanted to go down the ladder anyway, because of the carnivorous reptiles and the fact that the rowboat couldn't outrun a very distractable duck. The other option was to call the shuttle with a radio built into the railing of the walkway (presumably also for emergencies), but when they went to call it, Simon discovered that someone had been there before them and sabotaged the radio by cutting the wires.
Here's where it gets weird. Because while I was still definitely Simon, I started to attempt to repair the radio using the knowledge I'd gained from Circuit Theory. Which was definitely my college's Circuit Theory, not "the best medacad on Osiris", because I remembered working on my final project, with my pink-haired lab partner, in my (women's) college's engineering building on Earth, while still having no knowledge of being anyone but Simon. Then River also used my knowledge of Circuit Theory (without being the viewpoint character, so I have no idea how I know this) to notice something Simon had missed and point out a much easier way to fix it. (I have a distinct visual memory of her dress, for some reason- it was kind of shaped like the dress I wore for Changeling Halloween, with big poofy sleeves and a sash, but it had a bigger skirt that trailed in back and almost-but-not-quite a bustle, and it had a pattern of blue cherries on a pink background.)
The viewpoint was back to third person at this point, and Simon and River got the radio fixed, and then Simon headed back down the walkway to help Book carry something, but just then, this huge lizard-monster showed up. It was vaguely humanoid, but shaped more like King Kong than a person (very wide and muscley), and covered in diamond-shaped green scales. (I got the sense that they would've been much brighter green, except that all color was washed out on this horrible rain planet.) It didn't have any eyes that I noticed, but it had at least three mouths crammed onto a misshapen squarish head, with several rows of two-inch-wide shark teeth in each of them. It grabbed Simon in one arm, Book in the other, and roared, and the view changed to a sort of comic-book stop-motion (one still frame, then another a few seconds later, and so on, the way people do in movies when someone's taking pictures) as I got the sense that a commercial break was coming up (which was the first knowledge I had that this was fictional/a TV show, but wasn't surprising). I woke up just as the "commercial break" would have started.