The only thing I would add is a little depth to his third case: of nominally or lapsed Catholics who do not marry in a Catholic wedding. Consider the following case, which is very common:
A lapsed Catholic who is free to marry seeks to marry a non-Catholic, who likewise is free to marry. The Catholic has no particular desire, unfortunately, to practice his or her Catholic Faith. If the Catholic marries without benefit of the Catholic form of marriage, that marriage is treated as invalid by the Church, although -- as Father Hoffman says, it is potentially valid.
But before you say, then a Catholic should not attend that wedding, unless the Catholic party remedies this situation, let me explain something: there may not be any way -- in good conscience -- for the Catholic party to remedy it! Let me elaborate.
Suppose you tell your lapsed-Catholic friend, "look, we can fix this. Come with me to see Father Friendly, who will explain how you can be validly married. You can even be married at the park as you planned, since your intended is not Catholic, so whatever form of marriage s/he prefers can be an option -- with the bishop's dispensation."
Your lapsed-Catholic friend agrees, the couple meets with Father. In the course of that meeting, Father will explain everything, including that the Catholic party -- marrying a non-Catholic -- must make two promises:
Do you reaffirm your faith in Jesus Christ, and intend to live that faith as a Catholic?
Will you do all in your power to share your faith with your children by having them baptized and raised as Catholics?
Do you see the problem?
Here it is: we saw above that this lapsed-Catholic does not desire to practice the Catholic faith. Perhaps s/he does not believe in Jesus. Perhaps s/he has joined another religion, or simply has no faith at all.
The only way this marriage can be "recognized" is either the lapsed-Catholic must believe -- that is, undergo conversion -- or else, answer insincerely. (And don't doubt for a moment that happens!)
Does that seem just to you? Do you think that is the intent of Catholic norms on marriage, to say that if you lapse from your faith, you may never enter into a valid marriage?
At one time, a provision in canon law specifically said that someone who formally defected from the Catholic Faith was not bound to the Catholic form of marriage; that was intended, I think, for such situations. This provision, however, was deleted. Why? Because that deletion solved a knotty problem: Catholics who defected from the faith came to their senses, and sought to return to the faith -- and perhaps what helped them wake up was realizing they'd entered into a marriage (outside the church) hastily and without care, and now that marriage was a wreck. Alas, the marriage was presumed valid, and they had to go through the arduous process of asking for a declaration that it was otherwise -- i.e., null.
Since such situations often involved a lot of immaturity, the sense was that by treating such marriages as invalid -- for lack of form -- then the Catholic who is now back to his/her senses can either resolve the problem of a foolish (and invalid) marriage easily; or else seek the Church's help in that marriage being recognized as valid.
However understandable that concern was, it created a new problem which I highlighted. How is that to be resolved? Are we to press people to make insincere declarations of faith?