I'm not 100% certain that this issue is caused by W3 Total Cache, but I have good reason to believe that it may be.
Two days ago I updated W3 Total Cache for the website where I'm an admin. The WordPress home page is here. Since then, we've started to experience a noticeable lag between posts displaying on the WordPress page and posts displaying on our index page. (Posts are retrieved on the index page by calling
wp-load.php in the header.) As I write: I published the article "Legal problems may halt Underbelly telemovie" half an hour ago, which should show up at the top of the index page. However, the index page has failed to update and still has yesterday's top articles.
I also updated another other plugin at the same time, but it's trivial: i.e. a plugin to output the website contact form. This makes me think that the problem has something to do with my settings for W3 Total Cache.