Before Bruce makes his speech at the birthday party, he knocks at a wine glass twice, producing two differently pitched tones. In reality, it should be the same tone, because the pitch is defined by the level of liquid inside the glass.
When Batman grabs one of the men unpacking boxes of 'toys' from the shipping container, another one of the men begins walking towards the container to check on him. The boxes seen through the doorway of the container change position from one shot to the next.
In the scene where Batman saves Rachel and the Little Boy from the released Arkham maniacs, the boy is seen holding his arms around Rachel with his face against her chest. Yet when the camera angle changes he is sitting and facing in a completely different direction.
During the wide shot depicting the batmobile sitting idle atop the parking garage, a swift sweep of the SWAT helicopter's spotlight reveals dozens of cast and crew packed into the elevator waiting area.
You cannot open a water main and see water flowing through it. Water mains that feed uses including sprinklers are pressurized to over 150 psi. Opening a main in the fashion shown would have flooded the basement in minutes. Also, mains serving other areas do not pass though buildings.
The scenes set in Bruce Wayne's childhood and adulthood both feature 2000s-vintage automobiles. Similar time discrepancies are common in the DC Comics source material where it all exists in "Hypertime", an eternal present. This is done to keep universal appeal and prevent it from seeming dated. Comic books set in the "Universe" where Superman, Batman, Wonder Woman etc. live, have modern settings for both stories set in "Batman's 1st year" and stories set in "Batman's 11th year," for example. It is simply a convention that these characters are chronologically ambiguous.
If the microwave emitter really evaporates all water in the vicinity, in theory it should also kill everyone standing near it, as human bodies consist mostly of water. However, it is mentioned earlier in the film that the emitter uses "focused microwaves" specifically designed to target an enemy's water supply. For the safety of those operating it, the device was presumably designed only to affect water at certain levels of pressure.
The position of tree branches over the water well young Bruce falls in changes. The branches look one way (from the bottom looking up) when Rachel calls down, but it appears to be a different tree when Thomas Wayne lowers himself to rescue Bruce. This may be a deliberate, as the scene is a subjective view of a confusing, traumatic moment, when memory can become unreliable.
During the roof jump part of the Batmobile chase there is a police officer who orders Batman not to move on the bullhorn. He is the same actor that later delivers the line 'Can you at least tell me what it looks like?' as the Batmobile whizzes past him. (In mitigation, they could be twins.)
In the short segue scene where Rachel Dawes is driving to Arkham Asylum, the street clearly has three lanes separated by white dashed lines indicating a single direction of traffic, yet traffic is flowing in both directions.
In the newspaper article about Wayne Manor burning down, several factual, grammatical, and spelling errors are present. The article states that Wayne Manor has been in the family for four generations, but earlier in the film, Alfred says it housed six generations of Waynes. The article says in the third column that if Bruce was responsible for the fire, he will 'loose' millions rather than 'lose' millions. The word 'tinder' is capitalized in the photo's caption when it shouldn't be. In the article's second column, Manor should be capitalized. And at the top of the third column, the article says 'If it is ,indeed...' The space should come after the comma, not before.
During the discussion between Ducard and Wayne in the burning mansion, a member of the league drops behind Bruce and tries to kill him. Bruce quickly incapacitates him and then attacks Ducard. The league member just vanishes between the shots.
After the mansion has burned down, Bruce and Rachel are having a conversation on the property. At one point Rachel has her hand on the side of Bruce's face. In this part, the angle changes from being on Rachel to Bruce, etc. One angle, her hand is on his ear then in another angle, her hand is lower then when, the angle goes back on Bruce, her hand is not on his face anymore.
When Bruce's parents die, his stance is inconsistent; in one shot he is standing up then sitting down in another. This may be a deliberate, as the scene is a subjective view of a confusing, traumatic moment, when memory can become unreliable.
Ra's Al Ghul's name is pronounced "Rayshe Al Goole" as apposed to the "Roz Al Goole" spoken throughout the film. There are several interpretations of these characters and the film is no different. He is also not immortal. His name is simply pronounced the way it is spelled.
Being that the toxin had been introduced to Gotham's water supply for weeks before the finale, any time someone would have boiled water for anything, mostly cooking, they would have been affected. There would have been tens of thousands of people admitted to the hospital daily and the source would have been discovered almost immediately.