The Dad's death was the angel's punishment for not killing Fenton.
The dad couldn't bring himself to kill his own son demon or not. So he decided to leave it to fate on what should be done. During a routine Demon hunt, Fenton instead killed the Dad. The whisper he gave to Adam was warning him not to make the same mistake.
When Adam shook the FBI agent's hand at the end he passed the God Mission on to him.
Why else would he told him he was a good man when most people he and his father touched were Demons? Any other innocent people they put their hands on had no effect whatsoever.