I was putting on my helmet and noticed a small crack. I have never fallen with it, but have dropped it. Do I need to replace it.

On another sad note today, I stopped at a stop sign in a middle of a broken beer bottle and had a flat tire. There is a small cut in the tire (new pro-races). After changing the tire I rode home. It seems ok do I need to do any thing about this.

I am pretty sure the answers are yes to the first question and no to the second, but it never hurts to get a second opinion.