Logging calls might be a good measurement of how efficient your call center is, but are you really throwing money at your call center to support efficiency or is it to enhance the goodwill your company has with customers by providing great customer service?
Where does the value from your customer service investment go and where do you want it to go? Is picking up the phone enough? With your customer service investment, are you trying to address a quantity issue or a quality issue?
How well your customer service staff resolve a complaints is hard to measure empirically with call logs. One way to take a stab at this is by collecting data (electronically) on each call. For smaller organizations, a simple list of check boxes, perhaps in a spreadsheet, that will only take a few brief moments to complete will provide some added insight.
Also, training call center staff on how to effectively relate to customer service issues, especially the difficult ones, could make their jobs easier and less stressful. This will also enhance your return on customer service spending.