content visit counter

This is a problem with ALL cacheing modules and external caches such as Varnish. You should take a look at the Better Statistics module (https://drupal.org/project/better_statistics) since it allows view counting via AJAX. However, the count on each page will still be stale during the lifetime of the cache. For example, if your cache time is 5 minutes, the count will only be out of date for 5 minutes, but the number will be correct once refreshed since it was continually collected.

If you really need the count to be fresh on every page load, you could write a custom module that serves the count via AJAX. Check the issue queue for Better Statistics to see if someone has already written one.

Correction syntax