Deliberate mistake: When the penguin goes into the cemetery, he bumps a tombstone and it moves. Almost certainly a tribute to legendarily poor director Ed Wood, who Tim Burton later directed a biopic of - this exact thing happened in one of his films. (00:39:15)
Deliberate mistake: After Batman destroys The Penguin's controlling system and breaks the TV screen he is 4 meters away from a narrow alley. Shot changes and he's now downtown driving around the city, Then there's a POV shot of him driving towards the narrow alley again, though he is now many meters behind. Then back to shots of him driving downtown until he finally arrives at the narrow alley. It adds up for pace, but it's very awkward indeed.
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?