I personally find it concerning.

It not just sometimes but continuously that they sleep in his bed.

And as you said he seems TOO interested in them. His level of interest seems abnormal to me.

I certainly hope you don't find out anything like he or the kids are naked in the bed.

Does he do anything like shower with the kids? Does you EX believe that he, himself, is like a kid?

Does he give them money/buy them an unusual amount of gifts considering his low income?

All I can say is keep a close eye on the situation and be mindful of anything the boys tell you.

Maybe question the boys in an innocent way about what they do in daddies bed? (do not say anything suggest or imply anything sexual). For example ask for what they wear then they are sleeping dadies bed? Ask them does daddy read stories to you while you are all in bed? Sort of try to get them explaining a bit about it, but do NOT put words in their mouths, and do not make it sound weird.