What are some strategies to turn negative customer feedback into an opportunity for success?

We funnel all feedback--negative and positive--to our leaders to review.  We highlight the positives on "all-hands" calls as testimonials and examples of behaviors we want to reinforce. We have leaders review the negatives to dissect the issues, identify easy fixes when possible, discuss better approaches for handling situations, and create training opportunities.  In many cases, we reach out directly to the customer to discuss the situation to see how we can rectify it and save the relationship.

I would start with clustering it to identify the core issues. In a workshop, I would ask team members (including customer-facing ones like call center agent) to further elaborate on the core issues and prioritize them, f.e. on two dimensions "urgency" and "effort". Some of the low hanging fruits should be resolved quickly, to demonstrate that you take care of negative feedback, some of the more effective measures should be taken as strategic objectives.