What is the importance of body language in public relations and what are the most common mistakes in that?!

Well it's one of the most important aspect, it shows how sincere you are; one of the most common mistake which most of the people do is not making enough eye contact while communicating.

Body language is a form of communication like any other. It can be negative or positive, help drive a point forward, or show a lack of interest and desire. Body language is important because it is often what we conscientiously and subconsciously read in order to form our opinions of an individual, and is vital to first impressions as unreasonable as that may be. The mistake that I often see is made by the individual that has not properly familiarised himself/herself with the appropriate practices and customs specific to the culture in which they are dealing. As an example, eye contact is considered very appropriate and fundamental to communication, but may be considered as rude in others, or something as simple as crossing your arms while speaking. It is essential that we as professionals properly educate ourselves in today’s very culturally diverse business world in order to become more effective and respectful communicators.               

Body language do matters but I think your way of speaking and the choice of words is more important. Your way of speaking is most important that shows your confidence. I think the more you sit relax and calm rather than moving your body parts is important in communication. I don't think body parts while one speaks can be moved in a desire way so its better to sit relax and then answer without much movements of hands or legs or even head. 

Body language is a mean of communication you have to be the perfect in this skill also. you should have to talk with your complete relaxation and fully confidence, face to face with your eye contacts.