(クレーム（苦情を含む）
Claims (including complaints)


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Note added at 19 mins (2010-10-25 03:13:09 GMT)
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I believe that the word "クレーム" can also be translated as "claim(s)." I often translate it as such. By using "claims" and "complaints" in your above phrase, there is a clear differentiation between クレーム and 苦情.

(Customer service counters/departments/sections are often subjected to a myriad of claims and complaints!)

Here is an excerpt of the definition of "claim" from an online dictionary:
http://www.yourdictionary.com/claim
noun
a demand for something rightfully or allegedly due
a right or title to something: her sole claim to fame

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Note added at 43 mins (2010-10-25 03:36:35 GMT)
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Here is a "customer service" solutions website which uses both the words "claims" and "complaints" and explains both with reference to customer service.
http://www-01.ibm.com/software/data/cognos/solutions/custome...
Cognos solutions for customer service
Information, complaints and claims

By tracking and categorizing Information, Complaints and Claims, you can gauge the severity of various risks and prevent them in the future for better performance management.
Simply counting complaints will not adequately reflect the nature or risk of a problem. Instead, you should monitor the customer voice across three dimensions: frequency, customer segments and type of issue. For example, complaints about product quality are more critical than order identification errors.
Claims, such as compensation or replacement, also have to be addressed effectively. They are a direct cost to the business and, if poorly handled, lessen customer loyalty.
With the Information, Complaints and Claims decision area, you can set planning goals and scorecarding metrics for these elements of performance management: