When Ivo and Gerald Robotnik are dancing through the laser room, their suits protect them from getting hurt by the lasers. However, their heads are completely unprotected by the suits, yet they came out without a single scratch on either of their heads from the hundreds of lasers in the room.
Shadow and Maria listen to the Traveling Wilburys album featuring the song, "End of the Line" together. During this flashback scene, they're supposedly in 1974, but the Traveling Wilburys and this song would not be formed/released until 1988.
At the end of the 1st movie, Tom and Maddie brought all of Sonic's stuff from his cave to their house. But in this movie, it's revealed that some of his things were still in his cave. One of them was his pair of nunchucks.
In the flashback scene of Maria and Shadow, Maria plays a record (presumably "Traveling Wilburys Vol. 1" from 1988). The scene takes place in 1974. Shadow turns off the player in the present day and the needle is in the same position it would be if that song were to be played on the album.
At the end of the 2nd movie, Sonic referred to Tom as Dad. But in this movie, he was still referring to him by his name. Though it may be that Sonic called Tom his Dad just to show that he accepted him as his father, not because it's what to call him from then on.
In the Knuckles TV series, Sonic said, "Robotnik's gone, and there's no new battle to fight." But in this movie, he told Tails and Knuckles that they have to ask Dr. Robotnik to help them defeat Shadow The Hedgehog. Because of this, it's unknown how they found out that he was still alive. However, that part of the movie was shown in the 1st trailer. In the actual movie, Agent Stone was the one who told Sonic, Tails, and Knuckles that Dr. Robotnik was still alive.
In the Sonic X TV series, Professor Gerald Robotnik was killed by the G.U.N. agents. But in this movie, he was still alive, and he reunited with his grandson, Dr. Robotnik. This movie shares continuity with the prior live-action Sonic movies and the Knuckles TV series, not Sonic X, so inconsistencies with Sonic X are not goofs.
In a scene taking place in 1974, the song "End of the Line" by Traveling Wilburys is played on a record player. This song, however, did not exist until its release in 1989.
When Tom (James Marsden) is being carted off in the ambulance, the sound of the ambulance is the American siren, not the English siren.