irregular feathering what can cause this?

I have 13 3 week old babies that are with their broody mom. Up until today they have been in a large dog crate and it has been a constant battle! The broody either knocks the water over or scratches littler into the water so it was needing to be changed 3 or 4 times a day and on days I had to be gone it wasn't good b/c they would either have dirty water or no water when I got home. They are on medicated chick started (which was not my choice but all the feed store had at the time) On top of feeding and water issues they just plain ole didn't have enough room in there and the cage got dirty FAST and often. I tried my best but I know it wasn't perfect conditions. Today I finally got a spot for them outside in a run with mom. I noticed that their feathering seems to be off, like their feathers are growing faster than they are. Some look better than others but anyone know what could cause this? Can the change of environment help them? also should I put a light out in the little coop for them at night? So far the mom seems to keep the good and warm with her and I figure they will get under her if they are cold. any suggestions and advice are MUCH appreciated!!