I have done it, and still do it unconsciously. It can be something as subtle as simple look in your eyes or a facial gesture. It can be more obvious as an eloquent string of harsh words or even the tone of the words you speak. Nevertheless, telling them they're wrong, is the wrong foot forward. Nobody appreciates an attack on their intelligence, on their rational judgment, and especially their pride. You're looking for a positive outcome, and most likely going to receive a negative response. Why not just challenge them to a duel and decide it there?

Whenever you begin by turning it into an opposition of "smarter vs. dumber" you automatically begin a battle between you and the listener before you even start. >From this point on it is most difficult to make any impressions or change their minds in a positive manner.

If you are going to prove your point, do it very subtly. So subtly that they hardly realize it's happening.

When I am positive about something and want to get it across, I often use a statement such as, "Well, I'm sure I'm right, but who knows, I've been wrong before. I could be again". I am stressing two important facts in this statement. One, being that I am almost 100% certain that I am right, and two, that there is a slight possibility that I am wrong. This means that I am leaving room for doubt, but stressing the fact that I am sure. You will always come out on top by admitting that their is room for error. This will inspire your opponent to be as open-minded as you seem to be. It will make him/her think twice about admitting that they may be wrong in part or whole.

Nothing good can come of telling a person straight out, that he or she is wrong. You will only succeed in stripping that person of self-dignity and making yourself an unwelcome part of any discussion.

Final thought:

Don't argue with your clients. Don't argue with your Husband or Wife. Don't argue with an Adversary! Please don't get them all riled up by telling them they're "wrong"! Use patience, tact, and a little diplomacy!