Do not move CJ for 2-3 minutes. The display will be removed and the camera will start to follow and zoom into any activity going on (ie. Pursuits, fights, people talking).
Change the size of the moon
Shoot the moon with the sniper rifle and it will grow until it reaches a certain size when he will shrink when you shoot it again.
Go to the gym in Las Venturas, and through the bomb garage next to it. Stand in that alley and look at the building across the street to your right -- and you'll see people jumping and walking off the roof. It will only happen if you stand in that alley and watch it from there. It's pretty much a Lemmings Easter Egg since Rockstar North made Lemmings (the company was known as DMA then)
Funny License Plates
If you import a car at the docks, most but not all cars have plates that differ from normal ones. One says "our fergie", or "disco stu", and a really special one says "ea sucks". Try it out.
In Los Santos there is a wall painting with a heart, Mary and an angel on it and it says: Jesus Saves. In GTA 1 and 2 on the buildings where you saved it said the same thing.
Gant bridge easter egg
Get a jetpack and fly to the top of the gant bridge. At the top is a sign saying: "There are no easter eggs up here. Go away."
If you leave the game on and don't do anything CJ will sing songs heard on the radio. The songs you will most likely hear CJ sing is the songs on your favorite radio station.