1) Collect Star Bits at every opportunity. Not only will you be needing the lives you get (one more for every 50), but you will be using Star Bits in the Comet Observatory itself to feed the hungry Lumas.

2) Look around you as much as possible. Use the Remote's D-pad to switch camera angles. You never know what you might find!

3) You should open up Ghostly Galaxy and complete its first mission as soon as you can. This will free Luigi, who can then go and find some of the precious Power Stars. Well, that's the plan - what he ends up doing is getting a Power Star and getting trapped. He will send the Mail Toad a note and a picture for Mario, telling you where he is. It is then up to the player to find him and collect the Power Star.

4) Similarly, completing the game (i.e. defeating Bowser) should be a priority for those who want to collect all 121 Power Stars. That allows the Purple Comet to start roaming the galaxies. The Purple Comet gives a challenge - in very Donkey Kong 64 fashion - for Mario to collect a hundred purple coins, upon which he will receive a Power Star.

5) Once you have the first three stars from any (large) galaxy, the next time you go in there will be a question mark over one of the stars. That means there's a secret Power Star in that mission somewhere.