I've had that happen to my approximately 35 year old female blue crown a couple times in the past. She had a very poor diet before I adopted her and it took a long time to get her on a better diet. It still seems to come back once in awhile. It has never harmed her and I usually would help her by flaking the loose layers off with my fingernail. She took care of the rest by rubbing her beak on a cement perch she loves to clean it on. Couple of days later and she was back to normal. His beak does not appear like he has been "feaking" it. A term falconers use for the action of cleaning the beak by rubbing it on an object and I suppose it applies to parrots as well since they do it so much. Does he have a rough perch that he can rub it on? Cement or sandy or otherwise. Might want to get him one if he does not. Still, it is worth a visit to the vet to get checked out and get some advice on. They will probably condition down the beak to where you don't even notice it any longer.
As to the condition of the feathers that Laurasea mentioned above, his feathers look just like my male rescued blue crown. He over preens and nips off the ends of the feathers. I think it is more of a stress thing and he was like that when I adopted him. Worse, actually. He was partially gray from the downy feathers being visible. Over time, he has improved but it is still an ongoing issue. I recently came across a product called Avian Calm that clams that it helps reduce stress for birds but I haven't researched it enough yet to feel confident in trying it. If anyone here has used it or knows if it is a real thing, it might just help out both birds.
One last thing, to help him warm up to you. This sounds absolutely silly to consider doing but I have found it worked on other blue crowns, not just my pair. Stand a couple feet away at about eye level with him then slowly start bowing towards him over and over making a low noise kind of like you are saying "birrrrrrrrrrrrrd". Most likely, he will bow back to you and make a similar noise. I'm not 100% sure of what I'm "saying" to them but my pair will both respond to it in a positive way. I've done it to a couple young blue crowns in a pet store and they responded. And when I was house hunting, I toured a house for sale and they had a blue crown. I think I made the agent's day when I told her to watch this and did it to that bird and had it go from frightened to kind of curious and more relaxed. If you try it, I'd be very interested to hear what kind of a reaction you got.