Birds feathers do get a bit battered and start to look untidy, they will also fall out from time to time even when there is no apparent moult happening. I wouldn't worry just yet, that said it will never hurt but will always benefit to keep him as busy as possible but at the same time take any changes you make slowly, the poor things had enough strange things occuring lately with his new home.
If he ever does begin to pull his own feathers out, the first thing you will need to do is get him a full vet exam, they reckon up to and possibly over 70% of feather plucking is due to a medical or nutritional issue rather than psychological but I really dont think you need to worry from what you've said.
I'm glad you have his welfare as a top priority, he has fell on his feet with you
