Continuity mistake: In the opening, Penguin's parents look at the cage holding him. From the outside, his shaking is making the cage move slightly side to side. From inside, his shaking is not moving the cage at all.
Continuity mistake: When Oswald Cobblepot is in his crib as a baby, in outside shots the rubber duck on the string is swaying back and forth. In shots through the crib bars, it is dead still. (00:01:00)
Answer: It isn't. If you look at when he dies you will see that he has cuts on his face that are bleeding red. The blue liquid is more like a bile, probably similar to saliva.
What about when he emerges from the water and green blood comes out of his nose and then his mouth?