Census what's known as a 'Reverse ETL'. This is to say it can take data in your data warehouse and distribute it to your productivity applicaitons.
A good example is this is an incredibly easy way to get your product usage data into Salesforce. Your engineers connect their database to Census and then you connect it to anything else.
Sync your data to Salesforce and track your team as they move work forward. Set goals for timelines, response/cycle times, work in progress, and more. Any process, any object in Salesforce.
Finding bottlenecks in Salesforce is easy with Flowdometer, a free tool for time tracking and setting SLAs in Salesforce.
Use Flowdometer to be notified of process breakdowns as they happen
If you're not sure where to start with a dysfunctional team, start with repetitive work. Figure out how things are supposed to work, and where they aren't happening this way.