All 12 playable characters have dialogue in the game that goes completely unused. The audio references an object that's referred to as an Omochao-themed gate. This gate would've been opened via the use of a nearby Omochao. However, no such "Omochao Gate" appears anywhere in the game, and Omochao himself does not physically appear in any level of the game either.
Contributed by PirateGoofy
A lot of Team Rose's levels end at a much earlier point than Team Sonic and Dark's. However, through the use of glitches, exploits, or cheats, it's possible to go past the goal ring with Team Rose and go to areas that are only accessible to the two other aforementioned teams. The same thing can also be done in some of Team Chaotix's levels as well.

Interestingly, the characters of both Team Rose and Chaotix have fully voiced and functioning dialogue for these normally inaccessible areas.
Contributed by PirateGoofy
In the level Hang Castle, if the Eggman Statue is looked at while upside down, Neo Metal Sonic can be seen. This can only be seen if the player is playing as Team Sonic, Team Dark, or Team Chaotix.
When Team Chaotix's team blast is activated they are supposed to sing, but due to the team blast being too loud, and sound effects cutting it off, it's impossible to hear the singing during normal game play.
Contributed by ChiliDogs
The F Rank was supposed to be in the game, but was scrapped for unknown reasons.
After the fight against the Robot Carnival/Storm, Eggman will always say, "Don't get too excited, boys! Those were the easy ones!" regardless of the team being used. This is likely an oversight, as both Team Rose and Team Dark have female characters within them.
Playing as a different character and turning the camera towards Rouge will cause her to turn her head to look at you and wink.
Contributed by CupleaƱos
By holding A + Y (or X + Triangle on PS2) after having chosen a team and stage in the 2 Player Mode, the teams chosen will be in their metal states.
Contributed by SOGESNAKE