Sin vs. mistake
"What is the difference between sin and mistake? I don't think most of us intentionally sin so couldn't that be making mistakes?" Cool question, Anon, and thanks. In the area of morality, the word 'mistake' does not enter into the discussion. Either something is a sin or it is not. A sin is an act of the (free) will. It is either something I choose to do or to avoid. The Catechism clarifies that sometimes we use words or phrases like 'mistake' to avoid using the word 'sin'; but, we know better than to do that:
"Without the knowledge Revelation gives of God we cannot recognize sin clearly and are tempted to explain it as merely a developmental flaw, a psychological weakness, a mistake, or the necessary consequence of an inadequate social structure, etc. Only in the knowledge of God's plan for man can we grasp that sin is an abuse of the freedom that God gives to created persons so that they are capable of loving him and loving one another" (# 387).
So, any action that we freely choose to do which is morally wrong is a sin. Speaking to your second question, the Church teaches that "the morality of human acts depends on: 1) the object chosen (the action itself), 2) the intention, and 3) the circumstances of the action" (# 1750). Intentions enter into the moral equation as explained below. The basic points are that good intentions don't make evil acts good ("the road to Hell is paved with good intentions") and bad intentions can make good acts evil.
"A good intention (for example, that of helping one's neighbor) does not make behavior that is intrinsically disordered, such as lying and calumny, good or just. The end does not justify the means. Thus the condemnation of an innocent person cannot be justified as a legitimate means of saving the nation. On the other hand, an added bad intention (such as vainglory) makes an act evil that, in and of itself, can be good (such as almsgiving)" (# 1753).