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.
The Blog In Blog plugins authors should be able to look into that Undefined index notice for you.
In the meantime, you can disable WP_DEBUG in your production site so the notice is not displayed:
http://codex.wordpress.org/WP_DEBUG
I don't know why the the "Call Stack" lines are printed, though. The functions mentioned there are used to build the Open Graph meta tags in Jetpack. They will look for an excerpt to use as an Open Graph meta description, for example. Since there are many posts within a single page, the function is probably going through each post, but I'm not sure why the Call Stack is displayed. A Debug function like debug_backtrace must still be active somewhere on your site.