@DStens
I'm on Dreamhost, have installed many different test and production Zenphoto environments and have had no problems with any of them. Early on I found I had to apply the path stuff above to get things working, but after 1.0.5, I've had no trouble.
I have PHP 5 and FastCGI running on mine.
And when you show the example for "dreamhosters", is this for a subdomain arrangement? I don't think I've ever played with a dreamhost subdomain arrangement before, and I'm not sure how that would be configured. Anybody else have a guess? It may be the database connection in the subdomain is being referenced incorrectly.
I don't think it's Zenphoto the code. It's probably something in the .htaccess, database setup, or zp-config. Can we see your zp-config maybe - edited for passwords of course?