So, I think this is probably one of the biggest things we've learned.
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THIS IS A SIGNIFICANTLY DIFFERENT EARTH. This is definitely not Earth in the past, or the future. The landmasses have never been like this, and will not become like this in the future.
We also got a view of what a completed Gem colony looks like.
Next, we finally saw Yellow Diamond and her Pearl, and learned a bit more about their authority.. The writers slipped a racism joke in there, when Steven asked the CG Pearl if she knew YD's Pearl, and she responded "We Pearls don't all know each other."
Also in the communication with Yellow Diamond, she asks "Where is the Jasper assigned to you?" This seems to indicate that Peridot was actually the one in charge of Jasper, and not the other way around, as I had assumed.
Something else interesting, is that Garnet offered to fuse with Peridot, to help her understand fusion. I was excited to see that, but not surprised when it didn't happen.
We also saw Lion warping, and found out that, interestingly, the Gem base on the moon had air. I'm fairly certain that the gems have been shown not to need air, so I wonder why this is.
And Steven is 14?!? Whoa.
I'm also curious what the mysterious orb was in the Moon Base.
Beyond that, we learned that the Gem Homeworld is in another Galaxy.
And HOORAY FOR PERIDOT JOINING THE CRYSTAL GEMS OFFICIALLY!