Well, I eventually got around to watching this.
The adjusters can teleport through doors, but only if they're wearing their special hats. I think I went along with this while the movie was on, but in retrospect it is a rather silly plot device.
Not to mention the problem of how Elise was able to go through the doors with no hat!! (Which could have actually been very easily solved if they had just taken the hat from the man Matt Damon knocked out inside the toilet.)
Actually, the hats didn't have to be Fedoras. Police Helmets worked. He was told to watch out for anyone in a hat, or even a baseball cap.
It did start off very slow, and I also noticed the quick, quick, slow, which I agree kind of jarred; not sure I would call it "The Director's balanced pacing."
I forgot it was "based" on a PKD story, but I found it hopelessly romantically sloppy (which PKD never was.)
The Mind Readjustment was a little more sinister though; changing people's thought patterns. That seemed out of place in such a enormous piece of cheese.
I think they struggled to give it a suitably exciting ending.
That is quite interesting because Wikipedia says:
The final scene (on the rooftop of the GE Building in Rockefeller Center ("Top of the Rock") was filmed four months after the rest of the film had completed shooting and has a different ending than the original.
It sounds like your intuition was good.
Wikipedia also says:
Some reviewers identified Abrahamic theological implications
Only
Some? Did the others not watch the same film?
Destiny versus Free Will. Basically, if I have this right, God has a written plan for all of us and Angels make sure we stick to the plan. However, God is flighty and mercurial and keeps changing his plan on a whim (at least 12 times in this case, they said) and all this causes huge problems for his Angels to keep track. However, he still believes in true love and that wins out in the end. Despite being a very busy person, God quickly writes yet another new plan, begging the question of why we had all this running around, and the on-off Weddings anyway. And those Angels need a Union.
Dark City and
The Matrix have already been mentioned. The publicity for the film says it is a cross between
Bourne and
Inception. I'd say it was more of a mash-up of
Jumper with
The Butterfly Effect.
The
Doors (not Jim Morrison's "The Doors") were quite a good concept though, and that idea at least saved the film for me.