Did Jesus commit any sin pertaining to the Sabbath? Please keep in mind #4 (or #3 depending on the version) of the 10 commandments:

Exodus 20:8-11


  “Remember the Sabbath day, to keep it holy. Six days you shall labor,
  and do all your work, but the seventh day is a Sabbath to the LORD
  your God. On it you shall not do any work, you, or your son, or your
  daughter, your male servant, or your female servant, or your
  livestock, or the sojourner who is within your gates. For in six days
  the LORD made heaven and earth, the sea, and all that is in them, and
  rested on the seventh day. Therefore the LORD blessed the Sabbath day
  and made it holy.
  and


Deuteronomy 5:12-15


  "Observe the Sabbath day, to keep it holy, as the LORD your God
  commanded you. Six days you shall labor and do all your work, but the
  seventh day is a Sabbath to the LORD your God. On it you shall not do
  any work, you or your son or your daughter or your male servant or
  your female servant, or your ox or your donkey or any of your
  livestock, or the sojourner who is within your gates, that your male
  servant and your female servant may rest as well as you. You shall
  remember that you were a slave in the land of Egypt, and the LORD your
  God brought you out from there with a mighty hand and an outstretched
  arm. Therefore the LORD your God commanded you to keep the Sabbath
  day.


As we know from John 5:8-11 NIV


  Then Jesus said to him, “Get up! Pick up your mat and walk.” At
  once the man was cured; he picked up his mat and walked.
  
  The day on which this took place was a Sabbath, and so the Jewish
  leaders said to the man who had been healed, “It is the Sabbath; the
  law forbids you to carry your mat.”
  
  But he replied, “The man who made me well said to me, ‘Pick up your
  mat and walk.’ ”


Per the Pharisees via 
Matthew 12:10 NIV


  and a man with a shriveled hand was there. Looking for a reason to
  bring charges against Jesus, they asked him, "Is it lawful to heal on
  the Sabbath?"


The following list is from this site:


  Jesus gave at least eleven different reasons for apparently breaking
  the Sabbath 
  
  
  Pulling an ox out of a ditch on the Sabbath was permitted.
  Circumcision is permitted on the Sabbath.
  It is lawful to do good on the Sabbath.
  The precedent of David and his men eating the shewbread.
  Priests work on the Sabbath and are blameless.
  The ministry of the Messiah is greater than the ministry of the Temple.
  God desires mercy from His people and not sacrifice.
  The son of man is Lord of the Sabbath.
  The Sabbath was made for man, not man for the Sabbath.
  It is lawful to lead animals to water on the Sabbath.
  The Father works on the Sabbath.
  


Do we say that Jesus did not commit any sin based on the New Testament?  Or do we say that he did not commit any sin based on Mosiac Law?  

Just imagine if I commit a sin and someone says, 


  "Hey, you broke the law!"


and I say, 


  "I am [some blasphemous saying that I won't even type for example],
  I make a new law with my authority."


I can completely understand the Jewish concerns.
Part of the confusion as modern readers is that we miss what the Pharisees meant when they referenced "the Law." For the Pharisees, "the Law" had two parts. There was the "Written Law" (תורה שבכתב), and there was the "Oral Law" (תורה שבעל פה), which they claimed was also given to Moses at Mt. Sinai. You can read more about this in the Mishnah.

The Old Testament certainly does not prohibit anything that Jesus did; His whole life was lived in fulfillment of the (OT) Law. However, the oral tradition that the Pharisees also considered part of the Law did forbid many things that Jesus and His disciples did.

Regarding the Sabbath, the Mishnah contains a list of 39 classes of work that were not permitted on the Sabbath, per the "Oral Law." Many of these prohibitions were quite nit-picky. (For example, they could only walk a certain distance on the Sabbath.)

Jesus, for His part, showed very little concern (or respect) for the so-called "Oral Law," and constantly refuted it using the Old Testament. This was, of course, outrageous to the Pharisees, and this led to many conflicts between them.