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Yes.
I generally appreciate most movies like that on second watch. Twelve Monkeys, Unbreakable etc.
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V For Vendetta was like that for me. There's a hell of a lot of stuff that's hidden in subtly in that movie.
Also, perhaps strangely, The Lion, The Witch, and The Wardrobe. The first time I watched it, I was so caught up on noticing the similarities and differences to the book (it was one of my favourites as a kid) that I couldn't relax and just enjoy the film. But the second time (and onwards), I did.