Continuity mistake: In the scene where one of the "high council" is speaking (behind a desk or pedastal), there is a close-up shot of the highest ranking council member's face. In his nostril you can see a dry booger. They then change the shot and then come back to a close-up of his face. The booger is no longer there. Sorry if this is a bit gross, but I found it amusing.
Trivia: After the fake Dredd kills the judge and his wife in their apartment, the camera then cuts to a street scene in which Hershey is calling in their location as "at the corner of Burns and Allen." This is a cinematic tip-of-the-hat to the legendary comedy team of George Burns and his wife Gracie Allen. She also says they are "at the corner of Abbot and Costello" in the beginning.