I've have a lot of dreams in which I was watching new Simpsons episodes (of course).
In one of them, Marge and Homer sold Santa's Little Helper to a mysterious, wealthy stranger, and Bart tried to find out who they sold him to. And Lindsey Naegle helped him. I can't remember anything else about it.
Another one involved a new trend at Springfield Elementary in which the students went around riding tortoises, and it involved a scene in which some kid was at the dentist, but then the dentist turned into Cletus shoving a pepper mill down one of his kids' throat at a restaurant. The same episode also involved Homer watching a movie trailer about someone who rides a flying shack (much like Willie's) around, fighting crime. Then the actor from the movie appeared at the Simpsons' house, driving a white van, because Homer apparently owed him money.
Not all of my Simpsons-related dreams involving watching new episodes. In another dream I had, my mom was friends with Moe, and me and my sister went to his house for some reason. He lived in my hometown, in a neighborhood where the streets were not paved and they were grass. However, we found him dead in the basement, lying on a table (hey may have been underneath the tablecloth, but I can't remember). Then we went in the back yard, where Agnes Skinner's body was wrapped in a tablecloth (or maybe a tarp), and her eyes were wide open, as was her mouth. There was also blood all around her mouth, as if she had been eating human flesh. And for some reason my cat was running around his house, and she turned into a bunch of other cats. I also remember calling for a van to pick up the bodies (not the police, I called specifically for one of those corpse vans).
I have all kinds of bizarre dreams and nightmares (I still remember Agnes Skinner's terrifying face in great detail), but those are the only ones I can remember involving The Simpsons (aside from the occasional cameo by a character).