I agree the baby didn't look like their biological child either. I'm sure we will come back to that.
I think I'm even more confused about "constants" than before. I think I'll do some searching. Thank you both for your answers though!
EDIT: Ok, here's what I found. This is from that particular episode called "The Constant." I thought I would post it to refresh everyone. I remember it clearly now....of course! I feel like I need to watch last season over again....or maybe EVERY season!
Back from the "future", Desmond wakes up in Daniel's Oxford room. Desmond replies to Daniel that he was in the "future" for about 5 minutes. Daniel seems somewhat astonished that Desmond was "gone" for nearly 75 minutes and tells him that the more time he goes back and forth, the more it gets harder and harder as in his case the progression is exponential. Desmond then notices that the rat is dead, from a brain aneurysm. Desmond confronts Daniel about it, but Dan says that he doesn't know if Desmond is going to also die. Eloise's brain short-circuited, she couldn't tell the difference between the past, the present and the future as she didn't have anything to attach herself to: she did not have a constant. Daniel tells him about the need for Desmond to have a constant, something that is present in both times and that he sincerely cares about and can recognize. Desmond grabs the phone and calls his constant, Penny, but the number has been disconnected.
Later in the episode:
On the beach, Daniel begins flipping through his journal until he comes to a page that reads: "If anything goes wrong, Desmond Hume will be my constant.