Sonic Adventure DX is much better than Sonic Adventure 2 Battle in terms of glitches. There are no known glitches in the game. However, there are some minor things that could be considered to be bugs.
Chacron is a secret rival from the races, who is well-known for the way he spends the first half of a race simply snoozing at the start. However, on the Pearl Race, he doesn't do this! The Chao need to push a beach ball at the start, and he begins immediately without waiting. This could be a glitch in the game. However, it is also possible that it's just because the race is so short.
Shiny Jewel Chao
Shiny Jewel Chao are special breeds which appear differently on the GameCube and PC versions, and not at all on PS3 and Xbox 360. This inconsistent behaviour, along with the strange and unusual appearances of Shiny Jewel Chao, leads many people to believe that they are glitch. It is possible that they were never intended to be in the game.