I seem to have learned, after roughly a month's exposure, the arbitrary association between US coins and their denominations. It no longer seems to matter that the 5 cent coin is larger than the 10 cent coin but smaller than the 25 cent coin. Or that the coins don't clearly show their numerical value. I'm not looking any more; I just know.
No progress with the notes, though. How am I supposed to cope when all denominations are the same size, shape, and color? What does the Americans With Disabilities Act 1990 have to say about this? (Answer: there's no explicit mention, judging by the absence of the words "denomination", "money", "currency", "notes", and "bill".)
One possibility that occurred to me today: maybe US wallets have lots of different compartments for notes, so you can keep them segregated? I've taken to keeping my $1 notes separate from all the rest. I wonder how that will work as a coping strategy?