Steps Involved:
  1. Open SharePoint 2010 Management Shell by going to Start | All Programs | SharePoint | Microsoft SharePoint 2010 Products | SharePoint 2010 Management Shell (Run as Administrator).
  2. Run the following script.

Powershell Script:

 
##Get the count of all social comments created by the specified user for the specified URL using SharePoint 2010 web service in powershell
$uri="http://serverName:10736/sites/ECT/_vti_bin/SocialDataService.asmx?wsdl"
## $userAccountName is a string that contains the specific account name
$userAccountName="domainName\userName"
## $url is a string that contains the URL from where we need to count the social comments
$url="http://serverName:10736/sites/ECT/"
 
## Web Service Reference - http://Site/_vti_bin/SocialDataService.asmx
$socialDataServiceWebServiceReference = New-WebServiceProxy -Uri $uri -UseDefaultCredential 

[int]$CountCommentsOfUserOnUrl=$socialDataServiceWebServiceReference.CountCommentsOfUserOnUrl($userAccountName,$url)
Write-Host -ForegroundColor Green "Number of comments created by the specified user for the specified URL : " $CountCommentsOfUserOnUrl