Mr.McGuigan brought up this subject so many times during the movie that I figured that there would be a website somewhere discussing this (on the slightly more humorous side, while googling "doors" in the Godfather the results were almost completely FAQ's and walkthroughs for the Godfather game).
The first result...was sparknotes. I'm not sure if the use of sparknotes is controversial or not, but it did clear some things up for me.
What is written here, though, is really not much different from Myah's blog entry.
After reading the paragraph concerning doors, I felt really enlightened--I was just thinking, why didn't I make the connection before? The last scene is, as Mr.McGuigan would put it, a sledgehammer in the face about how doors divide women from men, and aren't/shouldn't involved in their matters.
Also, while looking for doors, I found this. It's long, but I've read barely one paragraph and already I feel like it will help us understand the movie better. It's almost like watching the moving again...with more detail, however there are some details in the movie that are not in the script as well.
Edit: I finished reading it, and it seems that this script has many variations- for example, according to the script, the "accident that was no big deal" is a crater from a bombing attempt, not a wrecked car.
It's also incomplete. There's a transcript here, but it's not as detailed.
I really wish there was more to that other script...it's more fun to read than the transcript...
but if you wanted to know what Sollazzo and Michael were saying in the restaurant in Sicilian, the transcript has the translation, wheras the script does not.
personally, I think the script is worth a read. Although it's long and incomplete, it's good for review and more details.
There already are things that I hadn't noticed in the movie written out in the script- such as how smitten Connie really is towards Carlo during their wedding.
I have scanned over the first few pages and the script says that Kay's reaction to the bustle of the wedding scene in the beginning is like "a young and lively thing in a gift shop". She seems extremely curious and I find myself relating her as a "woman with no morales" (loose modern interpretation of the scarlet woman) a lot during the wedding scenes. She seems overly curious and joking while talking to Michael and his family, and doesn't seem to care about sticking out with her red dress.
also, I looked up Hecate (relates to Katherine, which relates to Kay). In Greek mythology, she is the goddess of witchcraft, magic, the night, moon, ghosts, and necromancy, according to this.
She seems to be expressed both negatively and positively. this article says that although modernly she is expressed as a hag stirring a couldron, she is a beautiful and once revered goddess. She is a goddess who "helps us make transitions and new beginnings" (according to the above linked article).
I can link this a bit to Kay- she made a statement in the opening scenes, and then seems to be part of Michael's new beginning as the godfather when he asks her to marry him.
Also...the last thing we see is her face as the door closes.