Other mistake: When Batman is video calling the Riddler and passes the phone over to the D/A, you can see Batman's face still looking at the phone in the reflection of the Riddler's glasses.
Plot hole: During the shootout with Penguin and his gang at the warehouse Batman gets shot and falls to the ground. Penguin then creeps over to the spot he fell and realises he has disappeared and is in his car behind him. It is totally impossible for Batman to just disappear and get behind them without being seen, no matter the rain or firefight, that place was lighted enough and everybody was looking that way. (01:18:00 - 01:19:15)
Continuity mistake: In the funeral scene, Bruce Wayne's hair changes lengths.
Deliberate mistake: At the end of the car chase with Penguin Batman's car drives upon a ramp at high speed before the explosions occur but his car only appears flying through the air and landing 15 seconds after the explosions. That's quite a long jump. (01:23:33)
Answer: In "The Dark Knight," we see Gotham State Police setting up barriers. In short, Gotham has never been shown to be anything akin to the District of Columbia, probably because Gotham is never meant to be the capital of the country.