At the end of the Day X (at 6pm) sequence the 24-hour timer beigns, however later in the government limo (no exact time but some time after 9am) Eggman tells the President he has 24 hours to surrender, but the countdown timer has been going for more that 15 hours, so really he has less than 9 hours left.
In the final story, the ARK is heading towards the earth at an incredible velocity. However in the cutscene where Amy and Shadow are talking inside the ARK, if one looks outside any of the windows, the ARK is clearly not moving at all.
In the Intro to the Hidden Base mission the word "Imperial" in the subtitles is misspelled "Emperial".
During the cinematic after you defeat Big Foot, the "Do Not Enter" sign is reversed.
Because the game cutscenes were never properly re-animated from the Japanese version to match the English Dialogue, the characters are poorly lip-synced and often talk over each other (including themselves).
Eggman has a Spaceship inside his hidden pyramid base that fly's to the ARK which Sonic, Tails, Knuckles and Amy Hijack. There is no reason for Eggman to have this as it's already been shown that he has a teleporter which leads him straight to the ARK.
The Media and the Military continue to mistake Shadow for Sonic despite news footage having a clear close-up shot of Shadow with a spotlight shining on his face. It is also later shown in the 2005 game "Shadow the Hedgehog" that the Military knows who shadow is and the commander even has held a grudge against him for 50 years.
When fighting Shadow as Sonic in the Jungle, when you hit Shadow for a Second time he says, "I'm the coolest." This is extremely out of character for Shadow and it's unknown why this line remained in the game. Due to how out of character and poorly delivered this particular line is, it has become a meme in the Sonic community.
The Presidents Secretary said the incident (Involving the moons destruction) occurred 3 hours ago, the incident occured at 6pm, and at time she says it its now past 9am, more than 15 hours later