The PlayStation 3 Greatest Hits version of the game's box cover suggests that trophies can be obtained in-game. However, the game did not have any trophy system implemented due to the game being ported to the PlayStation 3 a year before Sony adopted the console's trophy system.
Contributed by Tuli0hWut
In the Xbox 360 version of the game, there is a bizarre game-breaking glitch that can be triggered. This glitch is not exclusive to this version, but it's most easily executable there due to the physical release of the Xbox 360 version containing an earlier build of the game that has not been updated to fix the glitch.

First, turn on the cheat codes for Low Gravity (#18), Infinite Ammo (#11), Never Die (#36), and Super Explosions (#7), and then start playing the Zombie Uprising game. When you unlock the Hand Grenades, go to a specific marquee on the map, aim correctly, throw a grenade behind you and jump. If done correctly, you will be launched onto the ledge. Go further into another corner of the building on the ledge and use a second grenade to launch yourself out of bounds. Once you successfully glitch yourself out of the map, you will fall into the void, and be respawned in the main overworld with the Zombie Uprising HUD still present (the actual location you are respawned in appears to vary with each copy of the game). From this point on, random events occur as a result of the enabled cheats and the game trying to run in spite of the glitching, including floating debris, surprise zombie attacks, or moments where you just float around. As the game continues to break down, all items inside of buildings will disappear, random items outside will vanish, and the sky will eventually turn a bright, blinding white. However, despite all of these worsening side effects, the killing blow can occur at any time. At a random point, a grainy, ice-blue silhouette will flash on a nearby wall, and within the next few seconds, the game will freeze, permanently damaging the game itself and rendering it unplayable.

This glitch, and specifically the silhouette, has come to be known as "The Freezer", and since its discovery had lead to the corruption of numerous physical copies of Saints Row 2 for research purposes. The Freezer effect itself is believed to occur when the game tries to spawn either a zombie NPC or the player's shadow in an invalid location, specifically after the player had previously glitched out of the Zombie Uprising map and back into the main overworld. The digital Xbox 360 version of the game is not believed to have this glitch, as it had been patched unlike the physical version.
Contributed by MehDeletingLater
NSFW - This trivia is considered "Not Safe for Work" - Click to Reveal
During a mission in "Eternal Sunshine" on the Japanese version,Spoiler: when you defeat Mr. Sunshine in the "Meat Packing Plant", there's a cutscene where "The Protagonist" kills him 3 times, then chops his head off with Mr. Sunshine's own machete. The Japanese version's cutscene omits the section where-in your character holds Mr. Sunshine's head and tosses it onto the conveyor belt.
Contributed by ProtoSnake
It is possible to ride up the walls of buildings with some of the motorcycles, though it is most easily achieved with the Kaneda or the Kenshin.
Contributed by Mass Distraction
On the DLC Map "Lost Island", there is a giant octopus floating off the coast.
Contributed by DrakeVagabond
In Pleasant View Area District there is a campsite and a small lake. If you cross to the other side of the pier you will spot a hockey mask, referencing Jason Voorhees from Friday the 13th.
Contributed by Funland47
The Ultor name and logo was first used in Volition's first-person shooter Red Faction. It is likely that this is not a coincidence, and it is considered that these two companies are the same group. Spoiler:Toward the end of the game, the player will even comment "you can go to Mars for all I care," referencing the future events that occur with the company in Red Faction.
Contributed by GradientDruid
It is possible to obtain Carlos as a homie once more after he has died, albeit in zombie form. After beating the Brotherhood mission "Red Asphalt", you can then unlock him by calling "Eye for an Eye", a business ran by Afro-Caribbean black magic performers who specialize in voodoo.

Carlos was originally put out of his misery by the Protagonist, after being found chained up and dragged along the road at high speed by a member of the Brotherhood. The Protagonist's gunshot wound is still seen in the head of the model for Zombie Carlos.
Contributed by oskachu
Following a few arrows dotted around on the prison island, you can come upon a large purple bunny doll that rises out of the sea. When shooting it, it just vanishes.

The bunny makes another appearance in Saints Row The Third.
Contributed by ummwat