Prankster Comets are no longer fleeting- once they're in a galaxy, they stay, and the missions generated from the comets can be played at any time- you are no longer forced to get the comet star to play the other levels again.
The first-person camera now lets you turn 360 degrees, rather than stopping at 180.
Checkpoints are now triggered by flags instead of an automatic save based on your level progression. This can be useful for some missions (particularly a few Cloud Flower Green Stars) that would require an exit from the level if the player failed past the checkpoint- here, the flags are avoidable.
Award Snub: Lost many, many GOTY awards to Mass Effect 2. Despite the same people giving those awards giving SMG2 10/10s, probably due to the first Galaxy racking up nearly unanimous GOTYs three years before, while the original Mass Effect was largely ignored in GOTY awards (also in 2007) despite being one of that year's best-rated games. Much like at the Oscars, critics simply decided it was Mass Effect's "turn".
Glamdozer is ridiculously easy, as long as you stay on the central grate below her on the other side of the planet. She'll keep running directly toward it if you hit her quickly. If you don't act quickly, she's a pain. Ironically, the developers seemed to think that Glamdozer was either hard or a Puzzle Boss (which she is, to an extent, but then again, all of the bosses are to some extent), given that she's the only boss that the Cosmic Guide can show you how to beat.
Squizzard, too, since you can just stand on a chunk of solid ground and spam fireballs; his projectiles can't touch you, and you can just unload a ton of hits and then reset your fire flower while he does his "injured" animation.
The Whomp King, who has rather easy to dodge attacks and an easy enough to hit weak point. While he is harder than he was in 64, they didn't make him THAT much harder. And they made him a boss in the final world of the main game, so he should be a cakewalk.
Throwback Galaxy. Is it a Nostalgia Level capable of making players weep with joy once they hear the Musical Nod, or is it proof that Nintendo is running out of ideas and is too lazy to make a new, creative level? Or was it a poor choice for a remade level, when some would have preferred Bob-omb Battlefield instead?
The game itself. Is it a sequel that's even better than the original game, just as good as the first with different levels, or is it inferior to the first game as a result of losing things like an explorable hub world and a compelling (for Mario) story, and for having too many borrowed ideas?
Contested Sequel: While it's near universally acclaimed, critics and fans are divided as to whether it's better than the original or not. The game did briefly manage to outrank The Legend of Zelda: Ocarina of Time on GameRankings, but eventually fell down below Ocarina into third place, unlike its predecessor.
The Green Stars. Upon unlocking them, the focus of the game shifts from finding exciting and interesting new areas to scouring old maps for the hidden Green Stars (which thankfully chime when you are close to them). Some require interesting acrobatic feats, but many of them are just in some pit or, most egregiously, right next to the gold star, as if to taunt players who were looking carefully for it through the whole level. This is also the point where the game turns into a Wide Open Sandbox as you explore and look for all of the stars. Plus, to keep their locations secret, all of them are named generically ("Green Star 1", etc).
There are the cases where there are multiple green stars in the same level. You can only get one at a time, meaning that there are some levels that by design you'll be doing over and over.
Game-Breaker: Spinning and ground-pounding gives you a homing ground pound. Fair enough, but then you learn that it works on Stars too. All those difficult suicide-jump Green star missions? Denied! Well, sort of. The range is still limited, so you'll still have to be in the right area.
The Cosmic Clones. They hound you endlessly. They may also qualify as Demonic Spiders (see above). Or perhaps Demonic Bats or Goddamned Spiders. In large or small areas, you'll often try to pass a previously-walked area, only to run into some Clones repeating the path you made just a minute ago.
The Octoombas, a.k.a. the little blue alien dudes that spit rocks. They were virtually harmless in the first Galaxy, but this game just had to make them so annoying. While they had a close-range antenna whip in the first game, now they spit rocks at you from a distance. They're all over the place, and they live just to knock you off ledges and mess up Daredevil Comet runs. They're especially annoying during the games against the Chimp. It veers so close to fake difficulty, the Chimp even lampshades it by saying that he'll need to find some more games so he can continue to enjoy your frustration. Just reading that line makes it all worth the while, though.
Goddamned Boss: Digga-Leg. You're supposed to use the Drill to burrow through the planet and nail him in the glass underside, but the problem is he's constantly moving around after the first hit, which wouldn't be an issue at all if the hitbox wasn't so ridiculously small. The only surefire way to not bounce off his legs instead of dealing damage is to position yourself and start drilling right before he flips over, which the Diggas he releases make a hassle.
Older Than They Think: Think this is the first game ever to have dark clones of yourself that mimic your actions and are lethal to the touch? Think again; by the time this game came out, Rayman already had it beat by fifteen years.
Nightmare Fuel: Sorbetti can be pretty disturbing, with his creepy grin. He also resembles a snowman's head rolling around on its body.
Gobblegut is annoying enough in his regular form unless you can figure out how to hit his bellyache bulges in midair. Just wait till you have to face a fire version of him. You can't touch his body without taking damage, making it very hard to take out his bellyache bulges during the short window you have open to you, and whenever he dive-bombs the planet, he leaves lava pools. Not to mention, the longer the fight goes on, the more his flying body gets in the way of the player's view, making it difficult to see where his head is and where the lava pools are.
Fiery Dino Piranha. Just as difficult as in the first Galaxy, and because he's the last boss in the Timed MissionBoss Rush level, by the time you get to him you may have only thirty seconds or so to work with, largely due to luck-based factors in the earlier fights.
Bouldergeist, also fought on Boss Blitz Galaxy, has the most luck involved in-battle, meaning you need to do perfectly on Dino Piranha, King Kaliente, and Major Burrows so you have as much time as possible for Bouldergeist and Fiery Dino Piranha.
Grandmaster Galaxy is something of a That One Level by itself. The Daredevil Run merely makes things worse, since you have to complete several challenges with only 1 hit point and no checkpoints. Heck, the Hammer Bros section alone is tough to do without dying.
Any level where Cosmic Clones appear. Special mention goes to "Cosmic Clones in the Chompworks", whose path to completion involves several spots where you have to retrace your route, thrusting you right back into the path of the pursuing clones.
For those who had horrible memories of it in the first game (particularly the fast foe comet star), the Cyclone Stone returns, and it's much more painful than before. Let this video speak for itself.
All of the Chimp's levels; it is extremely frustrating to die just 10 points away from the final total and have to do the whole challenge over again. The worst is by far Melty Monster Galaxy's Bowling Challenge: what would normally be the most enjoyable of the games is wrecked by the fact that you need to talk to him and pick up a Rock Mushroom every time you lose (and he has three lines of text, each of which takes about three seconds to display).
The already hard "Luigi's Purple Coins" is back, and they seem to have made it both easier (actual solid ground, P2 can help out, getting the star itself is not timed) and harder (The timer is reduced from 3:00 to 2:00, there are only 100 purple coins and you have to grab them all, and there are Cosmic Clones chasing you.)
The Speed Run on Boss Blitz Galaxy. Five minutes seems generous, but Bouldergeist is so luck based that he can singlehandedly waste most of your time. This means that you have to do near perfect on the first three bosses, get really lucky on Bouldergeist, and quickly finish Fiery Dino Piranha.