A lot of folks in here are confusing what we as the audience knows versus what, presumably, Peck knows. As others have said, given his knowledge and his probable powers, he oversteps his authority at every turn: in the first meeting, he tries to boss Venkman; in the second meeting, it's the cop; in the third meeting, it's the mayor. He's full of demands and ultimatums. Though I agree Venkman doesn't do himself any favors by antagonizing him, I don't think the outcome would have changed much if he had been more accommodating.
(Aside: I love that we're having this conversation 30 years after the film came out. I saw it 8 times that first summer and it's been one of my favorite films since.)