Hi, Snooty -- I literally just edit the shortcode out of the content space for the page where my listings appear and leave nothing in that space; then I enter the URL of our shelter's results search string into a plug-in I have called Page Links To. This just makes it so that the page (which used to be our pet listings page) now dumps the user at our Petfinder page instead.
Crude, I know, but I hate the thought of our users looking for our pets and getting that ugly error code instead! At least this gives them something.
When the Petfinder API is fixed I'll put my shortcode back in and we'll (hopefully) be all set again. . .I hope they fix it soon!