When Toby delivers the baby and holds it up, it has a normal belly button. A newborn baby would have at least part of the umbilical cord still attached, assuming Toby had even the equipment to cut the cord and tie it off, and given the circumstances in which the baby was delivered, we'd be more likely to see the baby still attached to the umbilical cord.
Toby states that when the pregnant woman's baby is born it will have "zero immunity". In actuality the baby will be born with the mother's immunity.
Cabe says they're having to wait for the CDC personnel to fly in from Atlanta. While the CDC is headquartered in Atlanta, they have field offices across the country. They would send personnel from the west coast as well who would get there long before anyone could fly from Atlanta. Also, Los Angeles being a large city has their own infectious disease specialists that are quite capable as well.
Walters parents are from County Cork in Ireland. The accent is not a Cork accent. To put in in context it's like someone with a Jersey accent saying they're from Alabama.
Other than the Infectious Diseases team (which is fully decked out), at no time does anyone don a face mask nor eye protection, both of which are readily available in most areas of a hospital.