Factual error: The police "clone" the cargo dock's computer, as though it were a cell phone, so that they can watch all the cargo traffic and see when containers disappear. In reality, to "clone" a computer would simply make an exact copy of that computer's hard drive at a specific point in time. In order to see what is happening on a specific computer in real time, it is necessary to install some sort of spyware on the target machine.
Continuity mistake: In the scene where Omar walks through some alleys on his way to stick up a corner crew, he is first observed carrying a double barreled shotgun with a wooden butt. A minute later, when he emerges from the alleys and dumps the drugs down the sewer, he is seen carrying a metal pump action shotgun.
Other mistake: When Chris and Snoop go to kill Bug's dad, they have their high powered nail gun once again, even after previously throwing it in the marsh with the guns. Bought a new one? Not likely as the reason for throwing it away in the first place was because the cop saw it. Buying an identical one would defeat the purpose of ditching it.
Audio problem: When Carcetti is talking to the Interdenominational Ministerial Alliance, there is a moment of silence after he announces that he'll treat them fairly regardless of endorsement. During this moment of silence, the shot changes to an angle where Carcetti is mid-speech, while the audio is silent. The scene resumes in sync with the audio as soon as the shot changes.