As far as the dirty pajama collar in that photo... If I didn't have a bib on my kids when they were eating jarred food, it would always end up in that exact spot. And if it was carrots or sweet potatoes, like it looks like Gabriel may have had, it left a stain that was impossible to remove. It very plausible that those pajamas were straight out of a washing machine and looked like that. So they weren't necessarily dirty at all. And I don't see a dirty mouth, he looks clean to me! His hair looks clean, no gunk in the corners or his eyes... he looks much more taken care of than random babies I see at the store.
I also am wondering... that hat she has on him looks like it was hand made, and it also looks pretty tight, like it was made for him when he was an infant. Obviously if that is the case, this hat was probably special to Elizabeth. It makes sense to me that she would have taken a picture of Gabriel in this hat to remember him by before she gave him to someone if that is the case.