The open mouth breathing could mean that something is stuck in between the nostrils and the choanal slit, but it could also be a respiratory infection.
The nose goes the sinus cavity, the sinus cavity goes to the choanal slit. When the duck's mouth is closed, the choanal slit fits snuggly against the glottis (entrance to trachea) and the duck breathes.
(Ignore the technical numbers and text, just look at the arrow)