Mouth troubles in babies
Thrush

Don't be fooled by the color of the inner sides of the gums where the upper molar teeth are going to be. The skin color here is normally very pale, and is sometimes mistaken for thrush by mothers who are on the lookout for it.
Cysts on the gums and the roof of the mouth
Some babies have one or two little pearly white cysts on the sharp edge of their gums. They may make you think of teeth, but they are too round and they don't make a click on a spoon. Similar cysts can often be seen on the roof of the mouth, along the ridge that runs fromfront to back. They have no importance and eventually disappear.
Eye troubles in babies
Discharge and tearing of the eye
There is another kind of very mild but chronic infection of the eyelids that develops off and on in the early months in quite a number of babies, most commonly in only one eye. The eye waters and tears excessively, particularly in windy weather. White matter collects in the corner of the eye and along the edges of the lids. This discharge may keep the lids stuck together when the baby first wakes up. The condition is caused by an obstructed tear duct.
The tear duct leads to a small opening at the inner corner of the eyelids, first toward the nose, then down the side of the eye socket and into the nose cavity. When this duct is partly plugged, the tears are not drained off as fast as they form. They well up in the eye and run down the cheek. The lids keep getting mildly infected, just because the eye is not being cleansed sufficiently by the tears. The doctor should see the eyes and make the diagnosis.
The first thing to realize about this condition is that it is fairly common, not serious, and does not injure the eye. It may last for many months.
What mommies should do

If the baby has an inflammation that makes the whites of the eyes look bloodshot or even pink, it is probably an infection, and the doctor should be called promptly.
Text source: Dr. Spock's Baby and Child Care -Beanjamin Spock and Michael Rothenberg