There are several normal things that make parents worry the first month. Here are the typical concerns:
Stuffy Nose. Infants around a month old tend to have a congested nose. This congestion leads to noisy breathing. Often parents interpret this as "wheezing". However, wheezing is actually a sound heard in the lungs and typically cannot be heard without a stethoscope. This nasal congestion drives parents crazy, but rarely bothers the infant. Using nasal saline drops (available at any drug store) and trying to aspirate any mucus from the nose is about all you can do for this congestion. Or you can ignore it since it is normal part of being one month old, and, remember, you do not have to fix normal.
Gas. And you thought your newborn was gassy? At one month old, it is surprising your baby does not float off into the sky because of excessive gas. See fixing normal for more on gas.
Fussiness. Babies at 1 month old are often more fussy than they were initially. From around one to two months old many babies can be colicky. We do not know what causes colic or how to fix it. It too can be considered to be a normal phase of infancy. These baby cry a lot and are hard to sooth. They tend to be gassy and parents believe the baby's stomach hurts. The severity of colic can be mild, very bad, or anywhere in between. Often there is a pattern to the fussiness, with early evening being the most common time infants get fussy. Strange things often sooth the baby, such as turning on the vacuum cleaner, turning the radio to static, or driving the infant around in a car. The good new about colic is that nothing is wrong from a health perspective with the baby. Colic goes away and the infant is fine. The most important thing about colic is for parents to find a way to maintain their sanity during this tough time.
Rash. There are two rashes that show up at this age. One is infant acne. This is related to exposure to mom's hormones when the infant was inside the womb. It presents as pimples on the infant's cheeks. Another rash is called seborrhea or cradle cap. It presents as dry, scaly skin on the scalp or flakiness in the eyebrows. With seborrhea there typically is also a red, prickly rash that goes down the cheeks, around the ears and down to the upper chest. Both of these rashes go away without treatment. However, if seborrhea gets bad, washing the infant's scalp with Selsun Blue shampoo every other night for a few weeks can help it to resolve.
Congratulations! One month down and only 215 more to go until she is 18 and leaves for college.