My favorite meta-joke in the Moonlighting series comes at the start of the episode "Somewhere Under the Rainbow" (aka the leprechaun episode). An announcer intones: "Tonight, on Moonlighting," and then there are thirty seconds' worth of clips from the episode we're about to see. The clips are very short, chosen seemingly at random, cut together out of sequence, and just make absolutely no sense at all.
This is a parody of a kind of opening that a lot of shows had in the '70s and '80s: an "on tonight's episode" trailer consisting of thirty seconds' worth of clips to whet our appetite for the episode. The concept made sense, but the way the clips were chosen and arranged, it was almost impossible to figure out what the episode was supposed to be about. The Stephen J. Cannell shows all opened like this: thirty seconds' worth of apparently random clips of lines that made no sense out of context and footage of stuff blowing up.
I don't know when shows stopped doing this kind of thing -- probably around the time that shows became more serialized, so they needed to start with a "previously on..." prologue rather than a preview of the new episode. It's one of those things that just screams "'80s TV," though.