Woohoo! A bit of searching found me a page that generates LibraryThing widgets for your blog; another bit of searching and I've finally found out how to add a non-standard widget to a Typepad blog (that is, one you can't just select from a list Typepad give you).
Look to the right-hand column and you'll see a randomly generated list of five books from my LibraryThing catalogue. Clicking the book covers takes you to their Amazon page (I don't like this but apparently it's a requirement of using Amazon's book covers), and clicking the text link takes you to the book's page on LibraryThing where you can see people's reviews and tags - including, where I've added them, mine.
Now I just want to sit up all night adding more books and reviews to LibraryThing (I've read quite a lot lately, having been sick in bed with one thing and another) and looking for new widgets to put all over my own web social places.