Quality needs to be built in to any project, not bolted on. A good project manager ensures that it is an integral part of every activity, and that every team member contributes.  Things start going wrong when time constraints occur, and there is pressure to concentrate on the core 'hard' deliverables.

While there are many, many components in delivering a quality outcome, there are two key activities which can assist in this regard.  Using either will help.  Using both is better:
  1. Implementing a Project Office
  2. Undertaking project health checks

Photo used under Creative Commons from LuMaxArt