If you go here:
http://seasonfresh.com/wp-content/portfolio/
...and click on 'vector art', it just goes back to my main page (which is what my site does if it encounters a 404 error).

I did some 'investigating' and found the album page here:
http://seasonfresh.com/wp-content/portfolio/index.php?album=vector-art

How can I make the album list page go to the right link? How can I make the thumbnails show? Do I have to make them myself?

Sounds like you need to edit your .htaccess file to have the right path. In your case, it's
RewriteBase /wp-content/portfolio

Did you just upgrade? If so, the .htaccess was probably overwritten.

Alternatively, in config.php, you can turn off the 'mod_rewrite' option.