One absolutely important role of Quality function which is not there in written in their agendas anywhere but which is always done by them is to take all stakeholders in sync and perform a consolidation of product unanimously before letting is QC cleared and okayed for release to customer. Why is it so important for them to engage all stakeholders and win their confidence is very crucial to avoid any confusions and conflicts occurring at a later stage after the product has been released.
Testing criteria must be made very clear and the exceptions highlighting is most important factor stating what is not under the scope of testing. Scope of testing has to sync well with the exact business requirements for which the product has been or is being built to cater to its needs. Getting into the shoe of end user and looking at the product functionality and usage as per his perspective is also very important factor for quality function.