Alright, I'm not sure how this happened, but the address bar is no longer reading what it should.

On this page: http://www.bmengini.com/zenphoto/
None of the gallery links work: http://www.bmengini.com/zenphoto/Dance/

I know that this address is wrong: http://www.bmengini.com/zenphoto/Dance/
And that it should look like this: http://www.bmengini.com/zenphoto/index.php?album=Dance/
but I'm not sure what's causing that.

The same happens for the individual photos.

Any ideas?

You have simple enabled mod_rewrite, but probably the server does not support that or you don't have a .htaccess file. You can turn it off in the gallery options.