Spoiler question about the private detective
Could she see the angels?
My theory is that she could not. Only the couple and the three friends could see the angels.
But then it would make a plot contradiction. That said, the Will-Smith-goes-mad clips don't have the angels. Then they are passed to the three friends for the board meeting. Would the three friends feel strange that the angels are not in the clips?
Then, that said, Will Smith was truly mad in the three friends' eyes (as he was really raging to the air in the clips.)
Maybe my words can't explain well, but I do think there are some flaw in the plot.