Ton’s issue is very subtle (and I suspect he knows how to work around it for a fix potentially), but Kevin, it looks like your site (I’m presuming you’re using doesn’t have the data endpoints. You’ll need the IndieAuth and Micropub plugins downloaded and installed. These should allow the app to authenticate and post on your behalf. (If I recall they should work out of the box with activation, but may have a few settings you can tinker with if you need.)

As a bonus, you’ll also then have a slew of other posting applications you can use to post content to your site. I did an overview of much of this at a WordCamp a while back if you want a video walkthrough/tutorial.

Happy to help you walk through it all if you like. I’m sure others can also help you troubleshoot in the IndieWeb WordPress chat.

It’s not a complete Goodreads replacement, but it’s a reasonable start. (And maybe Michael Beckwith will eventually release his WordPress bookshelf plugin that will replace a lot of additional functionality.)