[ryandrake]

Here's a simple example where the certain knowledge of an opponent's hand comes in handy:

Player 1: "Hey, Player 2, I'll trade my wheat for your brick."

Player 2: "I don't have a brick."

Player 1 knows that Player 2 got two bricks and a wood 3 turns ago, and he bought a road. So the one card that's left over is a brick.

Player 1: "OK, I play a knight development card, I move the robber to your plot, and I take your card. Lo and behold, it's a brick!"

[thaumasiotes]

You'll get the same effect by just looking at the board and noting who has the brick production.

[TulliusCicero]

No, you won't. It's entirely possible to have brick production but no brick right now. Have you ever even played Catan? This is basic stuff.