API. The silver bullet in the clip of advices

Is there an API development on your project, but you still have no quality control as a process? 

Is anybody responsible for the quality of the released product at your well established process? 

QA team complain about developers team not writing unit tests again?

To learn from mistakes or to use well-known decisions: what is better? 

I would like to tell about the process and team mistakes and to show specific examples of how to avoid different mistakes starting with projecting of testing framework and test automation tool selection up to API versioning and productivity measurement. 

And let them say that there is no silver bullet. Actually there is and exactly for your problem.