This is a list of bugs in Sonic 3D: Flickies' Island.
If you go into a Special Stage during invincibility, it's possible to come out of it with invincibility off but with the music continuing to play until the end of the Act.
In Diamond Dust Zone, you run into several badniks named Diamond Dust Zone Badnik 1. They are snowball throwing snowmen. Generally, all you need to do is roll into them twice. The first hit makes them into a block of ice. The second hit releases the flicky inside. However, if you run into one of the snowballs during the roll, you lose rings. Its possible to be hit a second time and lose a life without any opportunity to recover rings. This video shows this glitch.
If the Genesis is struck hard enough during gameplay or if a critical error occurs, the player sees a "You Have Found the Secret Level Select Screen" screen and the level select screen launches. It can also occur in an emulator if the player has a 3D Blast ROM open and tries to load a savestate from another Sonic game. Here is a video showing the both methods of accessing the screen. The music played is the Continue music, which is the results music in Sonic 3 as well as the "No Way? No Way!" music from Blue Sphere.
This happens because all of the exception handlers are set to jump to the "Congratulations" screen.