Corrected entry: Near the end of the movie, the Riddler gives Batman two choices; he can save the woman he loves, or he can save his partner. You can clearly see that both of them have tape over their mouths. Batman saves the doctor, and peels the tape away from her face. Then the camera cuts to Robin, and he has no tape over his mouth. If Batman didn't save him yet, and Robin's hands are tied, where did the tape go?
Corrected entry: The big question at the end of the film - Does Edward Nygma know who Batman really is? Once they see that Nygma is crazy everyone is confident that Batman's real identity is a secret. Unfortunately, they don't take into account Two-Face's large team of henchmen who stormed Wayne Manor, all of whom (presumably) now know that Bruce Wayne is Batman. Less than half of them were captured by Batman's underwater net, leaving several to spread the word of Bruce Wayne's secret identity.
Corrected entry: When the Riddler and Two Face sit down to play Battleship with the Bat-Boat and Bat-Plane, how did they know two ships would be coming? Robin did not exist until Batman was about to leave to rescue Chase, so technically the game shouldn't exist and the two villains should only be expecting Batman.
Corrected entry: After Batman rescues Chase and Robin when they were falling down the tube, they are very close to the bottom and Two-Face is suddenly seen standing on the railing that fell and broke earlier. How did Two-Face manage to get all the way down there? The tube is easily several hundreds of feet long.