Extra Miiverse Stickers
You'll begin with 28 out of 90 stickers available. Finishing Grand Prix mode with unique characters unlocks an additional 30 stickers, one for each character. The final 32 stickers are available when you defeat the various Time Trials staff ghosts.
Getting Rocket Boost
You can get "rocket boost" by pressing the accelerator button and when "2" appears, hold it down for a rocket boost at the start of the race.
Golden Vehicle Parts
You can unlock gold vehicle parts by satisfying the corresponding requirements, as indicated below.
Gold Standard (Kart) - Earn a rating of at least one star on every regular Grand Prix (150cc) and Mirror Mode race
Gold Tires - Beat every staff ghost in Time Trials
Gold Glider - Collect 10,000 coins
Gold Handle - Use the Wii Handle for 50% of your most recent 100 stages
In addition to the Mushroom and Shell cups that are available as you begin the game, you can access the tracks indicated below by placing first in the corresponding circuit, as indicated below.
Flower Cup - Clear the Mushroom Cup
Star Cup - Clear the Flower Cup
Special Cup - Clear the Star Cup
Banana Cup - Clear the Shell Cup
Leaf Cup - Clear the Banana Cup
Lightning Cup - Clear the Leaf Cup
You unlock additional characters at random, as you complete the various cups with a gold medal. There are a total of 14 characters that can be unlocked in this manner. Playing through the same cups a few times won't unlock additional characters, so make sure you earn the gold on each cup in the 50cc and 100cc classes if you want them all.