Round characters, by definition, are characters who change throughout the story. The opposite, flat characters, are characters who remain the same throughout the arc.
If you want to make this character more rounded, use his drunkenness and disjointed thoughts to get him into trouble a few times and then have him start trying to work through those problems. Not saying to eliminate them, but maybe have him discover some coping mechanisms in order to better manage his failings.
(There is also what's called a negative character arc, where a character changes by degrading and becoming a worse and less functional person. I'm doing that with my own MC in my story. Took a character that just seemed fairly well put together, but had one key flaw. A flaw that doesn't sound like a flaw at all when you first hear about it. I'm capitalizing on that flaw, illustrating why it really is a bad thing, and using it as the narrow end of the wedge to gradually chip away at the rest of her character. In your case though, I would have to say that since this character you are talking about is already so full of problems, it's best to make it a positive character arc and have him work through his problems.)