If he can't keep food down. Chronic vomiting (not just spitup) will keep your newborn from getting critical nourishment. It could be caused by several things, including intolerance to formula's milk proteins, reflux, or a neurological issue, so get it checked.
If he feels too cold or too hot. This could mean an infection. Take his temperature rectally every few hours, and call the doctor if it's below 97°F, or 100.4°F or higher.
If he gets a weird rash. Tell the doctor about extensive rashes or skin discolorations. They could be a sign of an infection or other problem.
If he coughs. Infants can sneeze and hiccup, but if they have a persistent or mucus-y cough or they look like they're having trouble breathing, call the doctor. This could signal a respiratory infection.
If he looks yellow. It's likely jaundice, which affects 60 percent of newborns and results when there's an excess of bilirubin in the blood. It's usually harmless but needs to be treated. Rarely, it can lead to a buildup of toxins in the brain and cause neurological damage.