I'm currently using WP Widget Cache to individually set cache settings for each widget.
I tried running Hyper Cache on top of this, but it overrides the sidebar displays, as it appears to cache them as well, no matter how I have widgets individually set to cache via WP Widget Cache. Therefore, Hyper Cache is unusable to me at this time.
Therefore, I would like to suggest that Hyper Cache have a setting to not cache sidebar content at all. Ideally, I would like Hyper Cache to cache the post/page content alone, sans header, footer, sidebars, which would never be cached unless one is using a separate plugin to cache them.