BDOW! (formerly Sumo) Share pulls its stats directly from the social networks, so they're 100% accurate.

If you were using another share plugin or using another reporting service, a lot of them will log clicks as shares, which would allow incomplete shares to be counted (people who click share then cancel when they are at the share window).

If the G+ numbers are fluctuating, that is a known problem with Google. Their response is to wait a few hours to "settle down".

To verify your numbers check here: https://www.sharedcount.com/

Additionally, if you are using mobile or secure http, you may notice that most Social Networks counts canonical URL's like

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as different URL's and it will not include into your share count. If you're currently already using this meta tag, make sure its using the the URL that you want to be counted. Here's an example of how to add a canonical HTML code:

Learn more about Canonical URL's.

Also for Facebook, to verify what its seeing and why specific information is being shared, use their debug tool: https://developers.facebook.com/tools/debug/