Jesus had to correct many people during His lifetime on earth. Many times it was the Pharisees. Sometimes it was the crowds that gathered to listen to Him. Often, it was His disciples. In this scene, all three groups were addressed at one time or another.
The Pharisees confronted Jesus because His disciples did not follow their traditions. His disciples did not wash their hands before they ate. Jesus's response was that a man isn't defiled by what goes into his mouth, but what comes out of it.
This is great advice for any of us, isn't it? Here, I do not believe that Jesus was saying that we should not wash our hands. Rather, the point that He was trying to make is that we need to watch our tongues, because what we speak comes from our heart.
Only a couple of verses later, Jesus clarifies this to His disciples. Evil thoughts, sexual perversions, lies, and murders come from the heart. Jesus was making the point that these defile a man.
What starts in our heart eventually comes out of our mouth. What comes out of our mouth can eventually become an action. This is why it is important to address issues of the heart.
So what do we do if we realize that someone we know has an issue of the heart? We should pray for them. The God that created the heart is able to fix the heart. In fact, He sent His Son so that our hearts could be changed.
What do we do if we realize that WE have a problem of the heart? We should also pray in this instance, as well. However, we need to follow our prayer up with action. When we feel like hating, we should make a habit of praying for the person who offended us. When we begin to think lustful thoughts, we should pray and read God's word. Remember, when we resist the devil, the devil will run away from us (James 4:7). We may find that, when we fix the problem with our heart, the problem of our tongue will soon be fixed, as well.