So a whole hell of a lot to dissect in these final two episodes. After thinking on it for some 12 hours, I think I have some ideas of what is going on. In some ways it's sort of like Quantum Leap. Here's my brief and simplified take on what happened, though a complete rewatch of season 3 will definitely help in piecing together all the little nuances one misses.
Simply, Cooper is trying to find and stop the pure evil entity known as Judy. In that mission he also wants to save Laura Palmer who, based on episode 8, is the opposite of Judy. He manages to do that based on the footage of Laura's body wrapped in plastic disappearing, and when Pete goes out to fish her body is no where to be found. That's in the Twin Peaks world we've known for 25+ years.
But in so doing this, Cooper also changes the present and/or future. A couple of quotes really sum it up: "Is it future, or is it past?" and "The past dictates the future." We see Cooper leading Laura through the woods twice and in both instances she disappears. He then travels with Diane to Texas and finds her working as a waitress in a diner called Judy's using the name Claire Paige and she doesn't know who Leland or Sarah is. But in this travel, several things happen: he and Diane stop at a motel, have sex, and when he wakes up Diane is gone and leaves a message to him (addressed to Richard) and she signs her name as Linda. There are a lot references to Linda throughout the Return, so I suspect on another viewing some hints of the significance of Linda will come to light. When Cooper leaves the hotel is is a different hotel than the one they arrived, he has a different car, and the motel is in a different town. When he goes to the diner to find Laura Palmer, Cooper's mannerisms are different too.
Then of course we get to the final scene where they go back to Laura Palmer's house to visit Sarah but there is no Sarah, and the people living there have no memory of a Sarah or Leland Palmer. We're not in Kansas anymore. I think Cooper's last question is the wrong one. He asks, "What year is this?" It's not a question of time but dimension. He may have saved Laura Palmer in one dimension, but her life is completely different in another: Claire Page.
Another hint of what's going on during the scene where Cooper and Diane are by the giant power lines: "You don't know what it's gonna be like--" "I know." They know they're crossing over to someplace else and that it could be different.
So what I think is going on is Cooper is traveling between dimensions trying to find the entity known as Judy. And that's how the series ends, sort of like Quantum Leap. Cooper is like Sam Beckett in that he's going to continue to jump between worlds (or time, in the case of Quantum Leap), trying to right what once went wrong.