The blood of the Kaiju is ammonia-based. Per Guillermo Del Toro:
"The second thing that the Kaiju do which is, they decompose and they release an agent called Kaiju-[blue] that completely destroys the cities, makes the air impossible to breathe. The blood is completely acidic. So they figure out that the base of fluid of the Kaiju is ammonia-based. So how do they neutralize it? But it takes a while because, first of all, it melts the pavement, melts the structures around it, makes a noxious gas. By the time they get to a Kaiju, the first few attacks, they can't even get samples or corpses or pieces to analyze it. The Kaijus are essentially triggered to self destroy if they fall. So it's a very smart weapon."
As seen in this video from Comicon prior to the 2013 release of the movie -
Ammonia is quite toxic to marine life, per this from Wikipedia:
The toxicity of ammonia solutions does not usually cause problems for humans and other mammals, as a specific mechanism exists to prevent its build-up in the bloodstream. Ammonia is converted to carbamoyl phosphate by the enzyme carbamoyl phosphate synthetase, and then enters the urea cycle to be either incorporated into amino acids or excreted in the urine. Fish and amphibians lack this mechanism, as they can usually eliminate ammonia from their bodies by direct excretion. Ammonia even at dilute concentrations is highly toxic to aquatic animals, and for this reason it is classified as dangerous for the environment.
Even though it is not usually toxic to humans and mammals, we can get what is called Hyperammonemia, which is an excess of ammonia in the blood system. It is a dangerous condition that may lead to encephalopathy and death.
It seems anyone caught up in the Kaiju-Blue aftermath would have adverse side effects. As Guillermo Del Toro stated, they are a very smart weapon.