My infant baby opens her mouth while sleeping, what is wrong?

Probably nothing: Babies usually breathe through the nose except for when crying, but if her nose is clogged up, she will breathe through her mouth. Make sure the nasal passages are clear of mucous by using the salt water nose drops and a bulb syringe. If you baby is comfortable and doesn't sound congested, no treatment is needed.

Maybe nothing: She may be congested. It may be nothing. Can she eat fine? Breathe through her nose when eating? If worried, then video her while sleeping and show it to your pediatrician to be reassured.