This will make the whole photo crazy washed out, but importantly, it will give you a very clear view of where the flaws are in the background.
Return to the Color Fill layer, and with a white brush (100% opacity) very carefully paint over those flawed areas until they disappear entirely.
Once you've finished, turn off the Levels layer, so you're viewing the photo in its normal state again. Turn the Color Fill layer off and on a few times to make sure you haven't accidentally painted over the baby in any places.