Since you asked:
Lutherans believe that Scripture alone has authority to determine doctrine; the Roman Catholic Church gives this authority also to the pope, the church, and certain traditions of the church.
Neither the Pope nor the church can "determine doctrine" in the sense that they can make it up out of whole cloth. They can reiterate, explain, or expand upon the Deposit of Faith, but they cannot contradict it at all. Public revelation closed with the death of the last apostle. All we can do is try to understand its implications.
If you want to see a good exposition of the Catholic view of Scripture, read Vatican II's decree Dei Verbum.
Lutherans believe that a person is saved by God's grace alone through faith alone in Christ alone.
Nothing in the NT says anything about being saved by faith alone. In fact, the one place the words "faith alone" are used says you are not saved by faith alone. That's in James chapter 2.
The Roman Catholic Church, while at times using similar language, still officially holds that faith, in order to save, must be accompanied by (or "infused with") some "work" or "love" active within a Christian.
This is a completely muddled and confused description of Catholic doctrine.
What we believe is straight from the NT: "Faith without works is dead ... such a faith has no power to save one" (James 2) and "Neither circumcision nor uncircumcision counts for anything, but only faith working through love" (Galatians 3) and "If I have faith enough to move mountains, but have not love, I am nothing" (1 Corinthians).
Thanks for your take on it. A lot of the differences seem like mostly semantics to me, but then again, I'm not a religious scholar by any means. I just rely on my belief in Christ and know God will sort it out in the end. ;)