What do you mean by "large amounts of feedback"? What do you mean by "manage"? What size of project? I'm going to guess at these for your question.
During main development usually the only people testing the game are the QA staff and others internal to the company. The entire development team plays the game and can also create feedback. They are managed through tracking software as bugs, development tasks, or similar names, and they're assigned initially to QA leads. QA teams add steps to reproduce the issue, then they're sent to the proper developer in engineering, animation, art, audio, effects, design, etc, and proceed to the process until they're eventually closed.
By the time it hits players with an open beta the game should be mostly finished and playable. The feedback likely should be small, coordinated by community managers and QA leads, and result in bugs or documentation.