In the first episode Meow claims that some large aliens are docile, but they turn out to be very hostile. At first this is assumed to just be because Meow is dumb. But 13 episodes later, with the revelation that pulling cosmic strings sends one to another universe, it becomes apparent that the reason for that is actually because the planet they went to was in an entirely different universe than one Meow went to when he first visited.
In episode 20, the Jaicro Empire abandons its big offensive against the Gogol Empire...solely because their leader Johnny bailed to play guitar in a rock concert. Are they really incapable of doing anything at all in his absence? Well how else would you explain them not already having conquered a foe led by incompetents like Admiral Perry and Dr. Gel?
Episode 10 focuses on a "Groundhog Day" Loop, specifically with the number 8. A Mobius loop taking place when the local calendar reads July 8th. This episode aired on March 8th, and the next hour was Daylight Savings Time for the eastern coast of the United States.
Paul got the idea of folding his universe from Catherine. Notice that the way he folds it is like a map, and that it never occurred to him that someone might plow the folds. That means that from the perspective of the inhabitants of the 2-D universe, it's still flat- drawing a straight line and then rolling up the map doesn't make the line not-straight. A triangle's internal angles still sum to 180 degrees, a circle's circumference remains pi times its diameter, and parallel lines remain at a constant separation. It's only curved from the perspective of 3-D observers. That means he isn't manipulating gravity, but rather using his knowledge of higher dimensions. In fact, Paul has no concept of gravity; gravity does not exist in a stable 2-D universe like Paul's, at least not gravity that can be described as the curvature of space-time. A non-trivial 2-D universe, that is, a universe that contains things other than a single black hole, must be exactly non-relativistic, i.e. the ratio of the gravitational constant to the speed of light must be exactly zero, meaning that either the gravitational constant is zero or the the speed of light is infinite. Any value for this ratio greater than zero, no matter how small, causes gravity to become infinitely strong and collapse the entire universe into a single black hole in an instant. Thus, the entire concept of someone creating a wormhole to take a shortcut through space is incomprehensible to him.
Dandy's carefree and lackadaisical attitude makes a lot more sense after the finale... He has the power to jump between parallel universes. He's never had to truly deal with the consequences of his actions because he's been escaping into another universe for his entire life, and so never developed any understanding of the concept of consequences. Blow up a planet? Leave a friend to die? Get turned into a zombie? Lose his ship and leave his crew stranded? None of that matters to him, since all he has to do is jump into another universe where that didn't happen. He may not even realize that reality doesn't work like that for anyone else!
The fact that each episode is headed by a different art director. Given the fact that each episode takes place in an alternate universe, it's fitting that the show itself Paints the Medium by looking slightly different, but overall similar. Just like Dandy himself, as Catherine explains.
The endings of episodes 7 and 21 still happen, even though the multiverse is destroyed and reborn. This is because time has no meaning between universes, only within them. An arbitrarily long period of time can pass in one universe during an instant in another.
Meow's family will never see him again after he dies in episodes 1 and 3.
For that matter, they become zombies in episode 4.
The characters remember every time that they die. It doesn't affect our heroes too much, because they tend to be oblivious to life, but it's really taking a toll on Dr. Gel and Bea.
Episode 24 reveals that Paul harnessed the power of a one-dimensional universe to warp into Dandy's universe. Cosmic Strings, which drag their pullers into an entirely different universe, look an awful lot like them...
In episode 4, everyone becomes a zombie, even the narrator. It's later revealed that he's God, which means that even God Himself became a zombie.
So... In the end of the series, the universe is reborn with no God, i.e. the Narrator. Assuming that the series basically restarts, that means most of the series will happen again. Including Episode 10, where the crew is stuck in a time-loop they're only fully aware of because God told them so...
However, episode 14 revealed multiplenarrators, so are they respectively different Gods, too? There is hope for Blockhead, Bonehead, and Pinhead yet!