DEAN YEAGER: Dr. Venkman, we believe that the purpose of science is to serve mankind. You, however, seem to regard science as some kind of dodge or hustle. Your theories are the worst kind of popular tripe, your methods are sloppy and your conclusions are highly questionable. You, Dr. Venkman, are a poor scientist.
The Dean is the first authority figure who Peter rubs the wrong way, but totally won't be the last. All through the movie, Venkman rebels against the powers-that-be. Of course, the funny thing here is that the Dean is right; Venkman is a sham of a scientist.
PECK: And may I see this storage facility?
PECK: And why not, Mr. Venkman?
PETER: Because you did not use the magic word.
PECK: What is the magic word, Mr. Venkman?
And now Peter decides it'd be fun to antagonize the EPA agent, really for no good reason. Yeah, Peck is kind of uptight and annoying, but it seems like Peter is rebelling against authority here just because he thinks its funny. It's kind of a personality flaw in Venkman that ends up having pretty dire consequences.
PECK: I want to know more about what you do here! Frankly, there have been a lot of wild stories in the media and we want to assess for any possible environmental impact from your operation! For instance, the presence of noxious, possibly hazardous waste chemicals in your basement! Now you either show me what is down there or I come back with a court order.
PETER: You go get a court order! And I'll sue your ass for wrongful prosecution.
Once again, Peck is a jerk, but it's not like the EPA doesn't have a right to be concerned about what the Ghostbusters are up to. Even Egon is worried that their containment grid might blow. Sure, this government regulator is a bad guy, but he does have some pretty legit concerns.
PETER: What happened?
POLICE CAPTAIN: Some moron brought a cougar to a party and it went berserk.
Throughout the movie, the police are shown as totally incapable of maintaining law and order. The idea of a demonic demi-god from another dimension on the loose is so far out of the Police Captain's frame of reference that he's pretty useless.
DANA: Are you the Keymaster?
PETER: Yes. I'm a friend of his. He told me to meet him here. I didn't get your name.
DANA: I am Zuul. I am the Gatekeeper.
Looks like even in Gozer-land there are rules. For reasons the movie never quite explains, there has to be a Keymaster and a Gatekeeper in order for Gozer to come to our dimension and do his Destructor thing.
POLICE CAPTAIN: We picked up this guy, now we don't know what to do with him. Bellevue doesn't want him, and I'm afraid to put him in the lock-up. And I know you guys are into this stuff, so I figured we'd check with you.
At this point, the Ghostbusters have become the authority figures. The police have no idea what to do with a possessed Louis, so they turn to our heroes as the authorities on all things weird.
JANINE: Oh no, hold on! I've seen TV, I know you can't come in here without a writ or warrant or something!
PECK: Cease and desist all commerce order, seizure of premises and chattels, ban on use of public utilities for unauthorized waste handlers, and a federal entry and inspection order.
Here's where the government hammer drops. Venkman's antagonism causes Peck to show back up with the law on his side. What do you think the movie is saying about government regulation as a whole?
EGON: I'm warning you, turning off these machines would be extremely hazardous.
PECK: I'll tell you what's hazardous. You're facing federal prosecution for at least half a dozen environmental violations. Now either you shut these beams off or we shut them off for you.
The ironic thing here is that by trying to impose order Peck is actually about to cause a whole lot of chaos. He's letting his personal grudge against Venkman undermine the whole purpose of the organization he represents. Causing a giant explosion and filling Manhattan full of ghosts is probably not in the EPA's mission statement.
PECK: I am Walter Peck, sir, and I'm prepared to make a full report. These men are consummate snowball artists! They use sensitive nerve gases to induce hallucinations. People think they're seeing ghosts! And they call these bozos, who conveniently show up to deal with the problem with a fake electronic light show!
RAY: Everything was fine with our system until the power grid was shut off by dickless here.
PECK: They caused an explosion!
MAYOR: Is this true?
PETER: Yes, it's true. This man has no dick.
Despite the trouble his rebelliousness has caused, Venkman still hasn't learned his lesson. He takes the audience with the Mayor as another chance to antagonize Peck. Luckily, the Mayor doesn't seem to like Peck anymore than anybody else, and as the ultimate authority in the movie charges the Ghostbusters with the task of saving the city.
RAY: Gozer the Gozerian. Good evening. As a duly designated representative of the state, county and city of New York, I order you to cease any and all supernatural activity and return forthwith to your place of origin or to the nearest convenient parallel dimension.
PETER: That ought to do it. Thanks very much, Ray.
Ray attempts to try his new Mayor-give authority out on Gozer, but it doesn't work out too well. What's funny here is the idea that any kind of Earthly power structure would matter at all to a chaos loving god from another dimension—well, to any god really. Somehow, Ray doesn't seem to get that.