The judge only has one rambling speech in the movie, and it goes something like this: "To continue, you've listened to a long and complex case, murder in the first degree. Premeditated murder is the most serious charge tried in our criminal courts. You've listened to the testimony, had the law interpreted as it applies in this case. It's now your duty to sit down and try and separate the facts from the fancy. One man is dead. Another man's life is at stake."
Now, normally, you might read those words and think, "Wow that's pretty dramatic." But if you check out the movie, you'll see that the judge delivers this speech with a tone of total boredom and fatigue. This speech sounds like something he wrote a long time ago and still recites at every murder trial. His words also suggest that this is an open and shut case that will be decided rather quickly. And when we first go into the jury room and see everyone voting guilty, this assumption seems pretty accurate.
As a character, the judge in this movie doesn't just represent someone who's bad at his job. He also represents the justice system in general, which can often seem tired and unsympathetic. After all, this judge has probably seen dozens and dozens of kids just like the one on trial. So it makes sense that he'd feel a bit burned out by his job. Now it's up to fresh heroes like Juror #8 to inject some much-needed sympathy and energy into the justice system.