In the S World, there's the Starshrooms. The green one tells you to "go, go!" The red one tells you "slow, slow!" And the yellow tells you to stay in control. Traffic lights much?
The game starts with the Star Festival, just like Super Mario Galaxy, even though that only happens every hundred years. Mario meets the Lumas and the other races of the universe for apparently the first time, even though he met them already. The Toad Brigade forms again. And at the end of the game, Mario doesn't seem to remember Rosalina, although she remembers him. Then you remember how the first game ended: The universe was destroyed and reborn. This game is the events of Super Mario Galaxy happening again in the new universe.
Rosalina:When stars die, they turn to stardust and scatter across the cosmos. Eventually, that stardust reforms to create a new star... and so the cycle of life continues. But the cycle never repeats itself in quite the same way... So... you'll see.
To further support this in later games, think over it; Luigi's Mansion has a system where the more money one gathers, the nicer the mansion one gets at the end, and in a Mario Kart released after the first Luigi's Mansion, Luigi's course has a huge mansion — the one acquired when one gets the most money possible. But in Luigi's Mansion: Dark Moon, he has a normal-sized house from not acquiring that much money in the first. It does first come off as a Continuity Snarl, but when one remembers, if the universe was reborn and everything happened again albeit a little differently, and Luigi isn't that brave in this game, that's a brilliant Continuity Nod — if Luigi wasn't as brave in the new universe's Luigi's Mansion, he wouldn't gain that much money! So of course the house would be smaller this time around!
World 2's Solar System: a yellow Sun orbited by a rocky gray planet, a molten orange planet, a watery blue planet, a rocky red planet, a swirly giant planet, a planet with rings, a green ringed planet spinning on its side, and a swirly blue planet.
Why is Lubba so large and tubby? Well, his color and eyes place him as older than most of the Lumas, though younger than Polari, and he's portrayed as an adult. Many stars expand toward the later end of their life cycles, before imploding at the end.
After you get the secret Star in Honeybloom Galaxy, you get a letter from the local Honeybees saying that they couldn't reach it. You need to wall jump to get to where the Star is, and as the Mario Bros. can attest to thanks to the Bee Mushroom, Honeybees cannot wall jump.
It's more implied than anything, but there's this cosmic force called the Gentle Pull that seemingly manipulates fate so that Mario succeeds against Bowser. It's a testament to just how truly powerful and terrifying Bowser is that the very forces of fate and destiny itself go out of their way to conspire against him, and how essential his defeat is that it constantly makes it so Mario succeeds.
It's less horrific than you think. The gentle pull is never really used as a literal force, and is more of a metaphorical one. Simply put, Mario and his friends desire to protect one another is so strong that somehow, they will always accomplish it. It most likely has to do with their Star Child status.
After Bowser Junior is defeated on World 5, he is never seen for the rest of the game, not even for the final battle. It's not explained why he doesn't come back considering that he did return for the final battle in the first game. However, before you fight him on his Boomsday Machine, you can see that under the fighting platform, there's a black hole. When the Boomsday Machine gets destroyed, Bowser Jr. is send flying off the platform and we never see him landing on another. So yeah, the black hole sucked him.
Nevertheless, as Bowser Jr. is seen in other Mario games, it's safe to assume that he escaped the black hole or found a way to escape such a fate. Neither Nintendo would kill popular characters offscreen in such a way.