If you have Missed Schedule Posts problems, the same problems are present on all related functions ... JetPack is a FANTASTIC PLUGIN but use same functions for "Scheduled Future Posts" and "Social Autoposts".
My plugin fix only "Missed Schedule" and not "Social Autoposts".
Is possible that after WP Missed Schedule fix the "Failed Future Posts" you may also unlocked the JetPack "Social Autoposts" and cause the publication of a double post.
However, I know from experience that the same problems also exist on the blog based on WordPress.com who not use certain "WP Missed Schedule" ...
WP Missed Schedule should not impact your "Scheduled Posts" or your "Social Autoposts" and feed.
The issue might be caused by a conflict with another plugin.
Do you have any other active plugins on your site?
Could you try to deactivate them, one at a time, to check if one of them conflicts with WP Missed Schedule and JetPack or causes the issues with your feed? (for example a badly W3 Total Cache configuration or enabled db-cache function ...)
I am afraid but this seems to be an issue with the JetPack features of WordPress. It doesn't seem to be related to WP Missed Schedule.
For fixing it you may be able to find some help in the other threads mentioning JetPack http://wordpress.org/extend/plugins/jetpack/
Do you know how wp-cron works? When someone visits your site, it checks to see if anything needs to run :) So having it manually be forced to run every 5 minutes doesn't really hurt WordPress.
I want to remind you: if we can't reproduce a problem, it's hell to fix it :/ I'm not being dismissive, just my hands are tied when a small group of people encounter a rare issue!
If you have others question sLa is very happy to assist you, but next time, before you post, please read the guidelines, otherwise your message will be dropped ;)
P.S. Nobody forces me to give assistance, and no one is forced to use my plugins :)