When Madelyn is taking her baby out of the car outside the clinic, she puts a baby blanket over her shoulder. A few seconds later, when we see her from the front while talking to Homelander, the blanket is in a bundle next to the baby. When the angle switches to behind her, the blanket is back on her shoulder.
When Homelander arrives at the faith expo, there is a pin on his uniform on the left side of his chest. He leaves the expo to confront Madeline, and his pin is gone. When he returns to the expo; he has a pin again.
Butcher steals a nurse's ID badge to gain access to the neonatal intensive care unit (NICU). However, the nurse appears to work in an adult unit. NICU access is very tightly restricted; hospital employees who do not work in the NICU generally do not have access to the unit.
When Billy Butcher goes to the cemetery and attacks the gravestone, his first strike reveals that the headstone isn't attached to the base, as it spins slightly on his first swing.
Right after Starlight asks her make-up crew for a private moment with her mother, direct reflection of a cameraman can be briefly seen from a mirror behind Starlight.
When Billy is drawing the V into the vial, Mother's Milk says that if he "gets air in there it could kill the kid". He is drawing the V from the additional port in the bag, and the only way he could cause an embolism to the child is to introduce air in the IV line below the drip on the other line as the bag already has air in it.