Should accomplishments be included in a CV? If so, how? I imagine most academics have done a number of unique things that are noteworthy, but might not clearly fit into the standard CV categories. Such things might include: 


Being featured in a high-profile documentary about one's research
Discovering asteroids or exoplanets
Significant contributions to open-source software
Designing/maintaining a public-outreach website 
??? 


Should these be featured in a "Miscellaneous" category, or somehow massaged into an existing category? Or, should they be omitted entirely? (If something should be omitted, what is the criteria for keeping/omitting it?)
Actually, I wouldn't worry too much about "categories" on you CV. Create new ones as needed. But yes, you should include such things - especially if they have been recognized by others. The bullets you give seem reasonable for inclusion. Perhaps the ones most related to your work should be higher up the list as should the more significant ones. 

You can say only a little or a lot, depending on the significance, of course. Some that you just mention might open discussions in any interviews. 

In general, if you think it is something good you have done, then list it. No one will know otherwise.