I have the same problem.
The issue is that Disqus has added an action to “loop_end” which is calling dsq_loop_end() from the plugin when the custom loop that runs for the featured posts.
The way to fix it is to avoid using the standard WordPress loop in the feature posts section, but use a custom query instead. Have a look at the last example in this section: http://codex.wordpress.org/The_Loop#Multiple_Loops_Example_1
Using the new WP_Query(…) method resolved the issue for me with a similar theme.
I can find the comment content in archives… It’s just actually putting the content back in the database. There isn’t an interface where I as admin can post comments with arbitrary dates and author names etc…