Thinking critically requires the ability to be flexible with your ideas. Being so set in your ways or thoughts that you can't be influenced by new information hampers your ability to be critical. There is nothing wrong with being passionate about your beliefs, but keep an open mind. If your learn something new, demonstrate critical thinking by allowing it to influence you if it's valid and makes sense.
Being able to argue your case effectively is one of the keys to critical thinking. Forming your argument requires you to look at all sides of an issue an fully understand them, so that you're able to answer any questions from other sides with authority. The act of gathering supporting data forces critical thought as you separate good information from bad. Demonstrate critical thinking by making a well-thought-out argument.
There is no room for narrowmindedness in critical thinking. You must demonstrate the ability to think critically by being able to understand why someone else has an opinion that differs from yours. No one holds a belief without having a reason for it. Being able to see the other guy's point of view and the reasons for it is an important part of critical thinking.
The ability to not only see all sides of an issue, but actually analyze them, is essential to critical thinking. Demonstrating this skill requires you to expand your research beyond that which supports your beliefs and to give the same attention to the differing opinions. A critical essay, for instance, should not only support your own beliefs, but give attention to all of the opinions that counter what you believe.