Complete the game to unlock Arena mode under the extras option.

Defeat Venom at the grand finale mission to get the Black Spiderman Suit as a unlockable.

Beat New Goblin/Harry to unlock him for gameplay
NOTE: This only works for the collector's edition of Spiderman 3.

You can't take a bridge to the other side because of invisible barriers. I have found a way to get past them. However, you are very limited to what you can do. First, go to the Manhattan Bridge because it is a long one. Go within barriers and be on the side of the bridge where cars are heading to the barrier and beyond (right side). Jump on one of the cars and immediately enter Photo Mode. Hopefully, the car will continue driving and will drive past the barrier. You are still alive and are able to move around, zoom in, and take photos. You cannot leave Photo Mode because you will be catapulted back to the barrier. You can go as far as the other borough that is heavily lighted in the night time. At a certain point (usually when the bridge ends), you will reach a gray screen, and the only thing you can do is push the Start button and start over.

After beating the main story collect 50 spider emblems to unlock the black suit spidey suit.

Play through the game and take EVERY bosses photo, and whatever gang members you want, but leave at least one. After beating story mode get any remaining pictures you haven't taken, and you'll get around 15 points. Save your game and reset your PS2. Load your game and you should hear and see the Villain Photo complete and gain another 15 hero points. Send them, save, and restart the process as much as needed.

Beat the main story and collect 50 Spidey Emblems to unlock the black suit again.