Audio problem: When Rachel seeks out Bruce at the end of the movie, Bruce says, "I was a coward with a gun, and justice is about more than revenge, so thank you." In the first shot, his head is seen from behind, and neither his mouth nor his jaw is moving. (02:01:30)
Visible crew/equipment: During the first board meeting at Wayne Enterprises, in two close-ups of Mr. Earle, spots of bright green light from the movie camera is reflected in his glasses. The same thing happens when he opens the door and sees Bruce. There is no such light shining in either room. (00:46:10)
Continuity mistake: The woman that shoots Joe Chill pushes the gun all the way against his chest. In the next shot, the gun is at least a foot away from his chest. The scene is shown in real time, and no one moves that quickly. (00:24:40)
Continuity mistake: When Bruce is thrown out the door by Falcone's thugs, he lands next to a white pavement stripe. In the next shot, he is much closer to the end of the stripe than in the previous shot. (00:29:20)
Continuity mistake: When Rachel drops by to give Bruce his birthday present, his hair keeps changing, especially his fringe.
Audio problem: When Batman brings Rachel to the batcave, he sedates her. The sound effects of his syringe device are off. Rachel begins to pass out the moment the needle is stuck in her and the fizzing sound of the actual medicine being injected is a couple of seconds too late.
Audio problem: When Bruce is thrown into the cell, the metal door makes a loud, distinct noise as it's opened and closed. When Ducard is about to leave, he knocks on the door to signal the guards. In the following shot of Bruce, nothing is heard, but when the camera cuts back to Ducard, the door is fully open. (00:03:30 - 00:05:30)
Factual error: When Rachel is driving to Arkham Asylum, traffic is moving in both directions, but the three lanes of the road are separated by identical white dashed lines indicating a single direction. In the US, 3-lane traffic (2 lanes one way, 1 the other) have the single lane bounded by a solid yellow line, with yellow dashes if you can pass, or a second solid yellow line if not. (01:29:30)
Answer: This is actually true to the comics, where a regular thug named Joe Chill was the killer of Mr. and Mrs. Wayne. There is no connection between this movie/series and Burton's "Batman"; they are separate takes on the same story, which is why things can be radically different. Burton chose to alter the storyline to give Batman an even greater reason to go after the Joker, that's his decision. Nolan chose otherwise in his presentation of the Batman legend, sticking to the original story.
Twotall