The game was originally intended to be more graphic than the final release, with the initial goal being to earn a T Rating by the ESRB. However, part way through the game's development the ESRB introduced the E10+ Rating, so the Development Team decided to aim for that instead, resulting in some of the game's content being censored. This included changing the Black Arms' blood from red to green, editing scenes of GUN Soldiers' deaths, cutting out Maria's death, and censoring some pieces of dialogue.
Contributed by CuriousUserX90
There were plans to have Sonic in the game's multiplayer mode although this idea was cut early on in development. The only thing that remains of him in the game's memory is his Japanese voice clips.
Contributed by Mr. Kite
A song created by Magna-Fi, "Who I Am", was originally intended to be used as the game's main theme song. This was later changed to "I Am... All Of Me" by Crush 40.
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After completing the "Space Colony ARK Mission", there's a cutscene of "The Eclipse Cannon" destroying the White House along with the city. The way it's presented is a very clear reference to Independence Day.
Contributed by ProtoSnake
G.U.N. soldiers will sometimes reference former head of Sonic Team, Yuji Naka, by saying "Mr. Yuji Naka is alright."
Contributed by ProtoSnake
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After completing the "Hero Mission" in "Westopolis", Sonic will say "Welcome to the next level". This was the original slogan used by SEGA for the Genesis.
Contributed by ProtoSnake
According to Takashi Iizuka, the game was created to appeal to the American market.

"The Japanese Studio was to develop a Sonic game in the standard style, and the US studio was to develop something different which could contribute to the Sonic franchise. That background generated the Shadow game as he appeared from Sonic Adventure. We wanted to offer other game systems to attract a different audience from traditional Sonic fans. In the US, first and third-person shooters were popular and we decided to go with a character who could work with them." - Takashi Iizuka, Game Director.
Contributed by CLXcool
The game plays out depending on what missions (Hero, Neutral, Dark) are completed per level. In total, there are 326 possible stories each with their own sequence of levels, cutscenes and unique name for each "ark".
Contributed by KidDivinegon
Two of the mini bosses in the game, Blue Falcon and Black Bull, take their names from two of the racing machines from F-Zero, driven by Captain Falcon and Black Shadow, respectively. As SEGA helped co-develop F-Zero GX, it's highly likely that these were intentional references to the series.
Contributed by gamemaster1991