I want everyone to know that I nailed it.
[spoiler]*I suspected Comstock was the same person as DeWitt before entering Monument Island, and knew it for a fact inside the Hall of Heroes. HoH actually spoils everything implicitly, because here Comstock has basically laid out his past history - and it’s identical to Booker’s. If you look closely at the loading screen, you can see that Booker’s birthdate is the same as Comstock’s.
*I figured that Elizabeth was Booker’s daughter pretty darn quick.
- I admit I did not figure out the whole Lutece thing. I figured those two were trans-dimensional clones of Mrs. Lutece and one of them was. Sorta. I could tell if the tiny, unclear images and vaguely-English accent of the voxphones and lone mini-movie were the same as the weird teleporting pair.
*Knew instantly that Booker’s debt wasn’t money - it was guilt. Moral debt all the way.
Things that do still bother me/I’m unclear on:
*The villains in the piece are mostly vague. Even Comstock isn’t that well defined as a character, besides being a mad dictator. Fink is an obsessive control freak but that really that interesting. Daisy Fitzroy has almost no character at all. This is something of a shame, because these three figures effectively define the central conflicts of the story. I say they should definitely have been better integrated.
- Comstock is definitely older than Booker; the wiki claims it was a side-effect of using the dimensional portals. More than that, however, he doesn’t seem that much like Booker. It’s not just his supreme arrogance where Booker is troubled and self-loathing. His behavior just isn’t what I’d expect even if Booker was a murderous tyrant. Aside from a few snarky comments, Booker doesn’t seem to care about wealth that much (and evidently hasn’t really used his abilities to get more), whereas Comstock is positively desperate for cash and puts it to an immense variety of uses. Booker is direct where Comstock is extremely indirect, even cowardly. Booker may harbor racist views to himself, but at the least feels no need to state them, where Comstock is positively bursting with self satisfaction on the topic. Booker doesn’t show the slightest ability to persuade, and isn’t very good with planning as far as I can see, whereas that’s basically Comstock’s great strength. I can think of answers to any of these objections, but it’s not well supported in the narrative. Even their voice actors are different, so they don’t even sound remotely alike.
The wiki says, “Like Robert, the device had an ill effect on Comstock as well, and he became delusional.” - did I just miss that voxphone? I didn’t see anything which led me to believe he was insane in any sense, except for being a total bastard.
*Was it just me, or did Comstock never particularly comments on religion at all? Aside from a few mentions of God, his religion definitely seems to be all about himself. Then again, I suppose worshipping yourself is the oldest religion of mankind. 
*We never learn who Anna’s mother was. Would be very interesting if Mrs. Comstock’s alternative-dimensional version was Booker’s wife. After all, he evidently had enough of a relationship to stay together and have a daughter he would then take care of. It’s unclear what happened to her, of course - she could have died or left Booker for some reason, though it’s odd that she’d leave her daughter is so.[/spoiler]
There’s a voxphone which says precisely this; he was peering into another universe - implied to be Rapture - and copying secrets of plasmids.
On Vigors:
While there are enemies with Vigors, I did have to wonder why they were so rare. Consider it: there’s plenty of Vigors to go around. Fink has a plant turning out vigors constantly, no fewer than one Vigor every few seconds. Columbis can be a huge city and still everybody could have multiple Vigors. And unlike Rapture, there were no Tonics to give passive benefits, which many would prefer to Vigors.