Successfully complete the game to unlock the Arena mode option in the Extras menu.
Collect all 50 Black Spider Tokens to get the black Spider-Man suit to wear whenever desired for as long as you want.
Play as the New Goblin (Collector's Edition):
Defeat the New Goblin in his first battle to unlock him as a playable character.
As Black suit Spider-Man, use your slow motion to dodge the King-Pin's attacks. Build up your "Rage Mode". Once in "Rage Mode" you can attack as normal.
To defeat Venom in the grand finale mission, hold L1 and run and hit the boxes which drive him crazy. By holding L1 while doing this, you will have more time to run while your opponent is in slow motion.
Defeating the New Goblin:
Go up to Harry and punch him ten or more times, then swing away. Do this repeatedly. If done correctly, you will defeat him.
There is a way to cut the distance you have to travel. Get to the Daily Bugle. Get in between two smoke towers. You can use your Spider-Sense to find it. Look in the direction you want to go, then press Square and tap Left Analog-stick Down..
Rival gang reward:
Choose any of the gang patrol missions (Apocalypse, Dragon Tails, H-Bombers, Waste Tribe) and defeat all of their marked territories that match their logos to earn 3 experience points.
As Black costume Spider-Man, you can find the meteorite fragments (small rock-like objects surrounded by a purple/pink glow) by listening for a pulsating sound. The louder it gets, the closer you are.