Both of these glitches require 2 players from what I've experimented.
Invincibility Glitch:
1: Obtain an invincibility power-up (Blue Plumbers' Badge).
2: Kill yourself without your partner dying, too.
3: Revive yourself before your partner dies and go Big Chill and repeat for your partner.
4: Activate Big Chill's guard (C button).
Voila!
NOTE: You only LOOK invincible. You will not actually BE invincible (meaning you will take damage, but this is worth the laugh).

Infinite Abyss Glitch (Very funny and makes you quit your game, though, but it is worth knowing):
!: 1 player dies and then revive the player when the live player jumps off a ledge, causing the first player to revive himself behind the other and away from the ledge before he dies again. 2: As soon as the other player dies and before the first one dies, revive the second one behind the first player. 3: If you don't fall through the point where you die, repeat step 2 until you do. If it is done correctly, then you will have one of your characters fall into an abyss of endlessness. Revive the other player and have some fun with your doom!

If anyone reaches the bottom or dies and gets defeated, please inform me of this.