Facebook

Solution A: create a different cache for Facebook

1. Go to W3 Total Cache settings (Performance) > User Agent Groups page.
2. While you are at it, tick Enabled for the predefined groups there. This solves the Mobile specific settings have no effect problem too.
3. Click the Create a group button at the top.
4. Enter Facebook as the group name.
5. Add this to the User agents field:

facebookexternalhit
facebookexternalhit/1.1
facebookexternalhit/1.0

6. Click the Save all settings button.

Solution B: reject caching for Facebook

1. Find the W3 Total Cache settings (Performance) > Page cache > Advanced section > Rejected user agents setting.
2. Add this as value:

facebookexternalhit
facebookexternalhit/1.1
facebookexternalhit/1.0

3. Click the Save all settings button.

The Facebook Crawler

facebookexternalhit/1.1 (+http://www.facebook.com/externalhit_uatext.php)
facebookexternalhit/1.1