Should have checked over at Calibre's 'frequently asked questions' for my problem with book covers showing up in new version of Kindle for PC.
(Question) The covers for my MOBI files have stopped showing up in Kindle for PC/Kindle for Android/etc.
(Answer) This is caused by a bug in the Amazon software. You can work around it by going to Preferences->Output Options->MOBI output and setting the “Enable sharing of book content” option. If you are reconverting a previously converted book, you will also have to enable the option in the conversion dialog for that individual book (as per book conversion settings are saved and take precedence).
Note that doing this will mean that the generated MOBI will show up under personal documents instead of Books on the Kindle Fire and Amazon whispersync will not work, but the covers will. It’s your choice which functionality is more important to you. I encourage you to contact Amazon and ask them to fix this bug.