I had a whole nother SA2B glitch topic, but since pruning...
NOTE: WHEN OUTSIDE OF LEVELS, GO UNDER THE WATER TO SWIM IN INVISIBLE WATER, USEFULL FOR EXPLORING AND CRAP
Go to Security Hall in 2P. Go to the lasers where the tunnel is. Have a good amount of Rings with you. Go as most to the right as you can, to the corner of the tunnel leading up. Jump, Glide to the lasers. IF you get hit, Glide back. You have a chance of going through the wall. Then, Glide to the left, and hold L to free the camera. Go to the box on the right to find a room. This is the room that you are never supposed to reach in 2P! This is where the Treasure Scope item is hidden.
In Death Chamber in 2P, go to the green room. If you took the normal path (from the main room) go to the path on the right. Reach the end. There is a torch on the right. Stand under it, hold your joystick to the wall under it, and hold A. You will move. Keep trying untill you see a shadow behind the torch. Jump if you are stuck in the process. When you are behind the torch, jump, and glide left. You will find an empty room. Apparently, this is the Chao Key Room, and there are no objects, and no escape.
In Egg Quarters in 2P, go to the green room and go to the room on the left. Do to same thing above in Death Chamber. You'll be in the blocked off path. There are no objects, and no escape. Pretty interesting how it still exists.
In Final Rush in 2P, at the end of the level, go on top of the tunnel leading to the Goal Ring room. Go as far as you can to the wall. Then, face up (vertical, up the ramp), Spin Dash, and jump. Then, go through the wall, (you can when you are high enough) but in an arc path, so you can avoid the room in the end. You will see a long slope. Go there, and you will see that it is the ending of the level in 1P. If player one gets there, the stuff starts falling. Die, and it continues to fall, causing lag all over. You can even push the stuff when it hits the floor afterwards.
Go to Wild Canyon in 2P. Go to the lonely statue thing. There is a chest and a pillar. Grab on the pillar, hold left, and pull down. When you get stuck, move right and left. Keep going untill you touch the ground, stuck inside the chest. Then, hold up lightly. You will walk left, through the wall. If you don't, press right a few times and try it. When you go through, you will find random objects below you. They are the objects used in 1P. You can find:
A floating chest
Odd pictures
Mystic Melody Door
OmoChao floating for some reason
Swirl tiles
Mystic Melody Temple.
Go to the Mystic Melody Temple and land on it. Then, press B. You're character will make a comment. With Tikal, you hear Knuckles talk, showing that she was originally based off of te Knuckles character. (obvious in the DreamCast version) With Chaos, it's Rouge's voice. (same as with Tikal)
Now, this is possibly the BIGGEST glitch in the game. In Dry Lagoon, in 2P, go to the statue in the pool. Go to the head. Climb on the wall above the statue, toward the corner of the head on it, pressing the joystick up and down. If you stop even ONCE in the process, you'll get forced back out. You will go behind it if you never stopped. Then, press A and B and A again to Glide through the wall. Go to the left to explore the normal level outside of it. Go in a sharp diagonal-left direction to find a mysterious pool. This pool has very shallow water, so you have to touch it very closely to go in it. There is a useless life bonus in it. It's in the middle of nowhere, floating, with nothing around it. The box is solid, there are floating plants, and vases you can stand on. There is a Mystic Melody Temple nearby.
In Aquatic Mine, in 2P, go to the top floor, where the wood piles are. Don't go to the one near the fan, go to the other one. Keep pressing A and B to Drill Drive through the wood. When you get inside it, punch or stop moving to fall through the floor. You can find random pools of water, and the water principle still applies from Dry Lagoon. There is a strip of water. Go to the end of it, Then, go down. You'll see wood pieces forming a little tunnel, and a ring of plants. Note that Aquatic Mine has no death pit, and you have to restart once you fall down. Funny thing is, there are water pools over water pools. You can go to the bottom of one, and surface swim inside it, Sadly, the whole entire rest of the level is gone, only the objects can remain.
Credits to The Dark Fox for doing stuff with me for this.