How can I tell if a Casablanca poster is an original or a reproduction?

That's an interesting question. I don't know the answer
*definitively*. Of course it ought to be possible to do rigorous
empirical tests on the paper & inks to see if they match the
properties of samples which are "known" to be of that era. But on the
other hand, I'm betting that such testing is likely to be more
expensive than the market value of the poster to begin with.

Probably not; there are too many copies.
This site will tell you something about older posters, also that
before 1977 they were usually folded, something that may be hard to
detect after 60 years:

http://www.mpag.co.uk/index.htm

This site may have a couple, at least you can see what the originals
looked like, as well as prices:

http://www.filmposters.com/catalog/search.asp

These are obviously reprints:

http://www.ricksmovie.com/store/store.mv

Here are some more originals (one assumes):

http://www.drnoir.com/

You can see the rest of Google Directory findings here:

://www.google.com/Top/Shopping/Entertainment/Television_and_Movies/Posters/Vintage/

HOpe that helps, Myoarin