Quality assurance demands perfection of work whereas customers require quick resolution of their queries. How can we create a balance between the two

You should follow Quality management in order to resolve this issue

if you really intrested for solving this issue ,then you should gave priority quality department same like executation department,& also start every job after cordination of quality depart,

Quality is prime concern but other hand time is essence.
we should focus quality rather than hustle bustle! off-course we should avoid time consuming activities.

First and foremost, the one handling customers should be well equipped with enough knowledge about the operation, it's do's and don'ts, the policies governing the operation and the consequence of her answer to every question the customer has in mind.
The employee should confidently deliver her answer to questions with sincerity in her heart but without having to sacrifice the welfare of the company, its product and it's people.
The customer would feel your concern if you would sincerely handle her problem.
If she is satisfied to your answer to her question, she will do a repeat business and would encourage other customer to patronize your company.
It is where my expertise is.
I am excellent in solving problems of customers.
More often than not, client would recommend me to handle their transactions.