Thank You Jeremy!!
Installing that plugin to disable the Open Graph meta tags has solved the problem for now.
To your other points - when both plugins were active, the blog-in-blog content displayed as expected, but the page was preceded by many instances of the warnings as shown above so the page content was many screens full down the page.
My server which was recently setup to replace an older one is running PHP 5.4.21 (the previous server was on PHP 5.3.x) now displays errors in tables with an orange header and then lines of the "Call Stack" references all printed out. This is probably some setting in my php.ini file that should be changed to prevent the errors outputting like this?
I've also posted on the blog-in-blog forum with the same question, so hopefully the developer there will see it and figure out a fix.
Thanks!