Do No Harm - S1-E20
Corrected entry: Kate catches Claire's baby as he is being born and hands him straight to Claire, all gooey and 'newborn', but the baby has no umbilical cord. There was no time for Kate to tie off and cut the cord, nor a time-lapse or scene-change that would have allowed this to happen.
Correction: I have watched this twice and both times and there is a umbilical cord.
Bowling255 ★