The "homing stomp" is a variation of the ground pound attack that isn't mentioned in the manual. When Mario is near an enemy, jump, spin, then quickly press Z. Mario will home in on the enemy, landing with a powerful stomp.

At the start of Shiverburn Galaxy, switch to first-person view, then look up and to the left. You should see three shadowy figures standing at the top of the ridge. This creepy trio follows you as you travel through the galaxy; whenever you look at that side of the background, they will be on the ridge, watching from above...

After you beat Bowser in World 6, you'll be able to switch between Mario and Luigi anytime on Starship Mario.

Beat Bowser in World 6 to unlock the Special World.

Collect 120 Power Stars, then beat Bowser in World 6 again. After the new ending sequence, 120 green Prankster Comets will scatter throughout the seven worlds.

When you unlock the Green Stars (collect 120 Stars and beat Bowser in World 6 again), a Rosalina head is added to the available icons you can choose for that save file.

The final galaxy appears in World S when you collect all 120 Green Stars. "The Ultimate Test" in Grandmaster Galaxy has star #241 and Comet Medal #49.

Beat "The Ultimate Test" in Grandmaster Galaxy, collect its Comet Medal, and deposit 9,999 Star Bits at the Banktoad to unlock the Prankster Comet named "The Perfect Run" in Grandmaster Galaxy. If the Banktoad never had 9,999 Star Bits, "The Perfect Run" won't appear until you deposit them, even if Mario is holding 9,999 Star Bits.