Theoretical-headcanon: Barry Berkman is on a spectrum. Disclaimer: I am not trying to diagnose him because I lack such proxy,il it's just my analysis based on my observations his character.
1. Literal thinking. One of the many traits common within neurodivergent people, especially of these who might be on autistic spectrum is literal thinking. Barry displayed such characteristic in the beginning of second season, while visiting a house of Mr. Kuzino who was mourning the loss of agent Moss. Mr Kuzino said that he wanted to kiss a gun, and Barry took it literally without realising that Mr. Kuzino used a metaphor for s*ic*de.
2. Autistic meltdown. As we can notice, Barry had tendency to heart himself physically when he feels angry, frustrated, ect. (slapping his head, face). Barry had a huge anger issues, and mostly he directed his anger inward (autoagression) but the scene in the car when he was slamming the wheel chair and his face repeatedly could be a serve as a displation of autistic meltdown. Also, the indication of autistic meltdown could serve a moment after Barry broke the glass after the performance in the theatre after he killed Chris.
3. Sense of alienation. The scene from the first season where Barry killed Ryan Madison, and the whole acting group decided to mourn his loss by creating a evening dedicated to Ryan, sending invitation through Facebook. "I don't have Facebook”. This phrase demonstrated that Barry in a way existed outside of a social and cultural norms.
4. Prone to be manipulated. I have a tendency to think that Barry was manipulated his whole life, as a person, as a soldier, as a k*ller.I can't compare him being manipulated as a soldier because it will unfold a greater scenes but Barry definitely was manipulated by Fuches, who exposed Barry's skills to his own advantages. Honorable mention: Sally and mr.Kuzino.
5. Lacking sense of "self" and compensating it through acting. For many neurodivergent people, especially these who high-masking, the experience of fragmented "self" is not uncommon. While Barry was a terrible actor, acting was an outlet for him, making it's possible for him to realise many important thing about himself through acting, while being comfortable because he wasn't expressing himself, he was acting which made it "appropriate" to others.
6. Desire to belong. His sense of alienation could have made him into a person whose desire might be to belong somewhere. Acting courses gave him this opportunity, and that's why Barry was devastated when mr. Kuzino cancelled his acting classes and big premiere in the theatre.
7. Inability to "read" the crowd: Back to the episode when everyone in the acting group was mourning the d*ath of agent Moss, showing their sympathy to Mr. Kuzino. Barry didn't puck up on the mood of the people around him, being solely focused on the future performance.
8. Special interests. Barry's passion to acting could have been seen as a special interest or hyperfocus that's very common traits amongst individuals who might be on the spectrum. Barry was so focused on acting, to the point of the exclusion of other aspects of his life.