These responsibilities include identifying and examining critical errors or omissions, and acting as a liaison with the public.
Most commonly, public editors perform this work through a regular feature on a newspaper's editorial page.
Because public editors are generally employees of the very newspaper they're criticizing, it may appear as though there is a possibility for bias.
Public editor columns cover a broader scope of issues and do not have an accreditation process, while in order to qualify as an ombudsman of any standing one must be a member of the Organisation of News Ombudsmen.
[1] At The New York Times, the position was created in response to the Jayson Blair scandal.