I've seen some parents blowing on their baby's face when crying. The baby suddenly stops crying but he looked very surprised. I wonder if this could harm the baby in some way.
Whenever you blow air (either through the mouth or the nose), some particles from these cavities are carried by the exiting air.
Always some flakes of dry nose secretion are expelled when you breathe through the nose, more if you breathe heavily or sneezes. (that is why some jurisdictions require cooks to wear surgical masks covering both nose and mouth).
Always some saliva droplets are expelled when you blow air through the mouth.
So when you blow air at the baby's face, you will always have some saliva being sprayed on the child. And this saliva will carry samples of whatever is in your mouth microflora, bacteria or food particles. (that should be avoided, but is not all bad - because having contact with the bacteria will stimulate the baby's immune system; just make sure baby is healthy and well-fed AND parent is not currently diseased).
Drying your mouth before that will reducetthe amount of droplets, but your saliva glands will produce more instantly because the dry mouth triggers the gland's activity.
Taking REALLY good care of you oral hygiene is paramount for the child's safety and health. That applies to kissing too. Also its a very nice habit for the child to acquire by example. Let the baby see that you are brushing your teeth (and enjoying doing that). - And keep the dental hygiene stuff away from his reach.
Do not do this if parent is currently under a respiratory or airborne/saliva carried disease. Absolutely no infecting babies for the sake of making them stop crying.