Continuity mistake: When Gordon gives Batman the Joker card, which is in a small, sealed, tight evidence bag, the card switches position in the bag between the shots of Batman taking it and him turning the card around. (02:05:05)
Continuity mistake: Almost at the end when Bruce and Rachel are talking where Wayne Manor used to stand, she puts her hand on his cheek/jaw/ear area. The position of her hand changes between shots, from having his ear between her fingers to having her fingers below his ear and so on. (02:07:10)
Continuity mistake: When Bruce is pinned down under the burning log, the position and amount of flames on the log keeps changing, including some consecutive shots. The amount and position of the debris by his head also changes several times.
Continuity mistake: When the young Bruce is trapped at the bottom of the well, there are several shots looking up from the bottom. In the first shot, branches are seen over the well. When the bats fly out of the well, there are different branches, and when Thomas Wayne lowers himself down to rescue his son, yet another set of branches is seen.
Continuity mistake: When the thug attacks Bruce in the beginning of the movie, the man grabs his hair, yanking it straight up. In the next shot, he's suddenly yanking it sideways. His action is shown in real time, visible on screen at all times, and therefore can't be corrected by saying it only takes a fraction of a second to move his hand.
Continuity mistake: When the prisoners escape a villain disguised as a SWAT team member places a explosive charge against the wall. As he comes down the stairs an explosive pack is already there, and he places his explosive pack on top of that.
Continuity mistake: When Rachel drops by to give Bruce his birthday present, his hair keeps changing, especially his fringe.
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