I think that Holden's perception of himself and his grip on whatever "sanity" might be seen as is a complex issue. There are some elements to indicate that Holden is aware of something not being right with his mental condition. The fact that he is narrating his account to someone who operates as a therapist is one such element. Holden must be aware of some condition with his mental state if he is relating the narrative of his life in the way that he does. Even as the mental issue might be ambiguous, it is clear that Holden is aware that his grip on a healthy mental state is lacking. He acknowledges behavior that is destructive and cannot give a clear or concise answer or rationale for it. Engaging in destructive behavior “just for the hell of it” or not knowing why he does something are examples of how he is somewhat aware of a loosening grip on reality and his perception of self. Holden readily admits that he is a good liar and thus is able to deceive others. The fact that he is honest about this with himself reflects that he might be cognizant that he is spiraling out of control from a mental health standpoint. He concedes that he might be depressed and is anxious about things. He understands that he has not processed his brother's death fully and when he sees Phoebe, his defenses go down as the hope of something better emerges. Even Holden's desire to be "the catcher in the rye" can be seen as a reflection of a loosening grip on reality. He seeks to be something he knows he cannot be.
Whether or not Holden is insane is a question that can arouse passionate debate. Holden might be seen as insane simply because he does not conform to social expectations. If a society is filled with inauthenticity and "phoniness," Holden might be ahead of the curve. Accordingly, Holden might simply be willing to maintain his own sense of self in a world that seems to take away individuality. However, I think that Holden is aware that something is amiss in his life and in his approach to consciousness. I think that Holden fully understands that there is something "off" in terms of how he functions in the world. This awareness might be where he understands that his grip on his mental state and a healthy approach to being in the world are not quite where they need to be.