Modules breaking or incompatible with external and aggressive caching

This is a question that had been asked before and discussed elsewhere. For instance, https://wiki.fourkitchens.com/display/PF/Modules+that+break+caching%2C+a... provides a list of modules that break the external and aggressive caching - some of them does not play well with normal cache either.

I need Drupal for Facebook and Organic Groups, both of which are listed as incompatible when external cache setting in the performance page is enabled.

What needs to be done to make these two compatible? Can we use block-level cache enable-disable to disable caches for these two and others like them? Is it possible to bypass external cache for any modules?

I would like to get the ball rolling here and then start posting in the drupal issue queues for the different modules.

Any suggestions / Help / Please!