Here are some glitches and funny things that I have found while playing the game:
Steel Fist Grab
First you'll need the Steel Fists, Tornado Uppercut, and Air Grapple moves. Get steel fists and go to an enemy that you can grab. Do the Tornado Uppercut and press circle in mid air. You will grab the enemy, despite you having Steel Fists.*
This one is sorta tricky and sometimes just happens on its own. Go to the city and get a vehicle (mainly a bus) and carry it to the ocean. If you throw it just on the gate, it will be boucing up and down before it lands back on the ground right in front of it.
I'm Drowning, I'm Drowning!
As you walk along a bridge in the city, people will be constantly falling into the water.
Go under bridge and destroy it. If you did it right, Hulk will rub his head and look around.
Bad Insurance Claims
When you are in the streets, cars will constantly be screeching off the road. Sometimes they will hit pedestrians on the way!
It's Raining Air-Conditioners!!
Jump on building with air-conditioners on it. Get as close as you can to them and jump without damaging them. They will fall off the building and into the streets. You may have to charge your jump.
When you have either or both Abomanation or Savage Banner unlocked, play as them. when you do moves that require grabbing, the object or enemy will look weird when you do it.
Get two police officers lined up. If the're lined up correctly, the furthest one will keep shooting the other one.*
Run up a building and do the elbow smash, then as you flip over, do an air dash. This can be useful when in a 'situation'.
He Did It!!!
When encountering a missile soldier, get behind a vehicle. He will still shoot at you and will destroy the vehicle instead of you.*
When you destroy a skyscraper, any cars around it will move around.
Rise From the Ashes
Again, when you destroy a skyscraper, some objects will be covered by the stuff that forms around the building. Walk on them and they will rise up.
THE Way to Destroy Cows
You can pick up a cow and throw it in the water.
In the hideout area, go to the very edge to a gate you cant cross. Use the shockwave smash to get the pole thats over there.
The Endless Climb
Again, in the hideout area, go to gate that you can jump over and press circle. you will start holding on as if you could climb it like a building.
Open This Door!!
Go to the church and attack the door. It will swing open and shut again.