This is something I had been wondering about for some time, and thanks to some expert help from the Thunderbird newsgroup (Bill McCartney in particular) I finally got to the bottom of it today.
Here is the procedure:
1. Export address book(s) as *.ldif file(s) and rename the file(s) to .txt
2. Use a program called Email Finder Pro to extract the addresses and rename the output file to *.lst - note that support for the program has been discontinued, but Bill kindly sent it to me, and since there don't appear to be any restrictions on distribution I have placed it here for downloading.
3. Download and install ListMaster Pro (LMP) .
4. In LMP, under File > Config enter your DNS Server IP (in my case this is shown at the top of this page) and your e-mail address (ideally this should be an address that matches your ISP).
5. Open the previously saved *.lst file (File > Load - change the file type box at the bottom to [*.lst] so the file will show up), then select "Verify all addresses".
6. "Sit back and enjoy the show", as it says in the LMP help file, which you should read, because it contains useful information on how to interpret the results.