Expert opinion is divided on the long-term effects of mouth breathing but there is definitely enough evidence to support the mal-effects of such breathing for you to be concerned. The following nicely summarizes the alleged effects, both anatomical and functionally on the quality of sleep.
Authors Full NameJefferson, Yosh.
TitleMouth breathing: adverse effects on facial growth, health, academics, and behavior. [Review] [88 refs]
SourceGeneral Dentistry. 58(1):18-25; quiz 26-7, 79-80, 2010 Jan-Feb.
AbstractThe vast majority of health care professionals are unaware of the negative impact of upper airway obstruction (mouth breathing) on normal facial growth and physiologic health. Children whose mouth breathing is untreated may develop long, narrow faces, narrow mouths, high palatal vaults, dental malocclusion, gummy smiles, and many other unattractive facial features, such as skeletal Class II or Class III facial profiles. These children do not sleep well at night due to obstructed airways; this lack of sleep can adversely affect their growth and academic performance. Many of these children are misdiagnosed with attention deficit disorder (ADD) and hyperactivity. It is important for the entire health care community (including general and pediatric dentists) to screen and diagnose for mouth breathing in adults and in children as young as 5 years of age. If mouth breathing is treated early, its negative effect on facial and dental development and the medical and social problems associated with it can be reduced or averted. [References: 88]
Thus there may be two major concerns: 1) the mouth breathing itself and, 2) the cause of the mouth breathing, obstruction to airflow either as you suggest in the nose itself or commonly further on as a result of enlarged adenoids, obstruction that can be associated with disordered sleep.
I suggest that you speak with his doctor about your concerns and, together, consider requesting a second opinion by physicians at the nearest Children’s Hospital, skilled in the complete evaluation of chronic airway obstruction, all the potential sequelae of it including but not limited to disordered sleep and the “long face syndrome”, and the definitive treatment of it, in addition to medication to relieve nasal obstruction. From your description, the request for a second opinion is not at all unreasonable.