The second series of the BBC One show drew complaints from viewers over the “shocking” sound quality, with people citing “mumbling” and inaudible dialogue.
The director-general said he took “all such complaints seriously” and had asked BBC Television “to look into this matter”.
Minutes from a meeting with the corporation’s governing body, the BBC Trust, document Lord Hall also saying BBC Television has been asked to “consider any immediate issues as well as identifying any lessons for future commissions”.
Happy Valley actress Sarah Lancashire was recently the subject of speculation over whether she would return for a third series.
Lancashire - who plays tough police sergeant Catherine Cawood - was quoted as telling a Sunday publication that she “wouldn’t want it to go to a third series”.
A spokeswoman for the show dismissed the comments as old and said there had since been discussions between her and Happy Valley writer Sally Wainwright.
A spokeswoman for Red Production Company, which makes Happy Valley, said: “Sarah and Sally have been talking and Sarah would be very keen to revisit Catherine Cawood.”
The series, which is set in and around Halifax and also features War And Peace actor James Norton, has been a hit and has regularly drawn in more than seven million viewers.