I can't see this at work and I'm trying to rember what you're talking about but all I can recall is the equivalent scene in the sequel, when he talks about all the HATE! just BOILIN UP, GATHERIN underground, etc.
William Atherton (Peck) said that for years after this he couldn't go anywhere without kids yelling "dickless!" and adults wanting to pick a fight with him
One of my favorite scenes in one of my favorite movies. The clincher is how Peter doesn't even try to appeal to the Mayor's sense of decency with an inspiring speech, which has to have been the temptation for the writers. Instead he goes right for the voter angle. Little things like that are what makes Ghostbusters a classic.