"Then the scribes and Pharisees who were from Jerusalem came to Jesus, saying, 'Why do Your disciples transgress the tradition of the elders? For they do not wash their hands when they eat bread.' He answered and said to them, 'Why do you also transgress the commandment of God because of your tradition? For God commanded, saying, "Honor your father and your mother"; and "He who curses his father or mother, let him be put to death." But you say, "Whoever says to his father or mother, 'Whatever profit you might have received from me is a gift to God'--then he need not honor his father or mother." Thus you have made the commandment of God of no effect by your tradition.'"
According to Mark 7:2 the religious leaders "found fault" with the fact that Jesus' disciples ate without first washing their hands. The fact that they object to something as trivial as this suggests they could find no fault with Jesus' teachings or other actions.
The tradition of the Jews (particularly the Pharisees and scribes) was to wash their hands before eating. Additionally, if they had been in a crowd where they may have come in contact with an unclean person, then they washed their whole body. It is important to understand that the scribes and Pharisees regarded their traditions as equal in authority with the law of Moses.
Thus, they ask Jesus why His disciples transgress the tradition of the elders. Since they believe that their traditions are as binding as a commandment from God, they probably feel that they've finally got Jesus right where they want Him. After all, He could not deny the actions of His disciples, which they deemed to be sinful.
While it is true that Jesus did not deny the fact that His disciples had violated tradition, He did defend their actions by attacking the Jewish evaluation of tradition in general - "Why do you also transgress the commandment of God because of your tradition?" (Matt. 15:3). There is nothing inherently wrong with traditions as long as they do not interfere with obedience to God's commands and as long as they are not elevated to the status of a command from God. The Jewish traditions, however, were often corrupt in both of these ways.
Christians must be exceedingly careful not to allow any man-made traditions to gradually be considered doctrine, even if the tradition is right in and of itself. To elevate a man-made practice to the status of a command from God is presumptuous and will lead to condemnation (cf. Deut. 4:2; Rev. 22:18,19). For example, in our worship assemblies it does not matter to the Lord whether we begin with a prayer, a song, or a Scripture reading. Most congregations will have their own tradition in this regard, and such is acceptable as long as they do not come to believe over time that the only way to begin a worship assembly is in the manner that they do and those who do otherwise are in error.
In Matthew 15:4, Jesus quoted from Exodus 20:12 and 21:17 regarding honoring one's parents and not cursing them. These were commands of God. However, the Jews had derived their own tradition in an effort to avoid fulfilling these commands. Jesus explains their wicked tradition in Matthew 15:5 - "But you say, 'Whoever says to his father or mother, "Whatever profit you might have received from me is a gift to God."'" Instead of taking care of their aged parents, they would greedily invoke this tradition which allowed them to claim that all of the money they would have used to provide for their parents had already been promised to the Lord's treasury. This was an empty tradition and was used by Jews who were selfish and lacking in love to the extent that they would rather keep their money for themselves than to spend it on their parent's needs.
Jesus exposed their wickedness in this tradition they had established. The law clearly demanded that parents be honored (i.e., submitted to and obeyed), but children who are capable of providing for their parents and fail to do so are not honoring their parents but are subjecting them to begging or starvation (cf. I Tim. 5:8). Also, although one may have never technically cursed his parents, to selfishly follow this tradition was in essence to do such and consequently be worthy of death.
"You have made the commandment of God of no effect by your tradition" (Matt. 15:6). Their man-made tradition had cancelled out or nullified God's command. Any tradition that does such is sinful (and the Jews had many such traditions - cf. Mark 7:13)! Any human tradition that nullifies God's word (or is elevated to the status of God's word) must be shunned (e.g., creed books, catechism, the Book of Mormon, etc.).
Although Jesus has not yet answered the specific question posed about uncleanness, He has proven that traditions of men are not authoritative. Thus, Jesus has established the principle that just because a tradition is violated doesn't mean that sin has been committed. In fact, some traditions should be violated in order to avoid sin!