TRY THIS FIRST before troubleshooting!
In 99% of all cases, share count issues are caused by third party caching plugins and services which lead to incomplete and half done MashShare update or installation or to a stuck of the share count. So your first steps should be:
Purge all your caches, including CDN/ CloudFlare (or similar services) whenever you update a plugin, update its settings or install a new one.
Also specify in your caching plugin and cloudflare cache that the cache will per refreshed periodically from time to time.
If the cache is not refreshed you will notice that the share count stuck and is not incrementing at all!
If you are using a plugin like autoptimize for minification of the MashShare related JS files make sure to exclude first these files or to disable the minification process at all. So you are able to test if the issue is caused by the minification process or by something different.
Possible related JS files are:
MashShare Share Buttons Plugin
Floating SideBar Add-On mashfbar.min.js
FB LikeBar Add-On jquery.cookie.min.js
Network Add-On mashnet.min.js
Analytics Add-On mashga.min.js
LikeAfterShare Add-On lashare-fb.min.js
PageViews Add-On mashpv.min.js
ShareBar Add-On mashbar.min.js
If you have cleared all caches and CDN or the CloudFlare cache, also clear your browser cache as it also may contain outdated files.
If you already have done that and the issue is still not resolved continue troubleshooting