What are the best ways to manage small short-term projects/tasks (nondepartmental goals) that resulted from meetings, VOC & audit reports etc?

There are always things that need to be done at the company level, that cross department lines. In these situations I would recommend a "go to person", i.e. Chief Administrative Officer. Whether you are large enough to hire the position or it becomes part of the tasks of a current employee, the function is needed. If no one is assigned these tasks, they do not get done. The person should be a senior manager or senior project manager that can move easily between departments and understands your business.