I'd like to talk about Ghost Busters chronologically, addressing events roughly in the order they are presented in the film. I endeavor to touch mainly upon narrative structure, character arc, and thematic content.
Ghost Busters opens on a conceptually instigating event, presenting a world in which the presence of ghosts, while perhaps not widely accepted, is plausible and established.
The first post-title sequence establishes Peter's nonchalance about the subject matter. He treats it with little respect, using the business to get women. His skeptical jester-like approach to the business of paranormal occurrences is in contrast to Ray, who is an overzealous believer.
While it may initially seem that Peter's character is an attempt to infuse comedy into an otherwise straightforward paranormal adventure film, I'd argue that the balanced relationship between these three is constructed to perfectly exploit comedic archetypes. Every Jokester needs a straight man, and it is the contrast out of which the comedy is based.
This is also utilized to uniquely portray three distinct comedy types. Peter is sarcastic wit, Ray is slapstick (overzealous, exuberant expression), while Egon is obviously deadpan.
This may speak to the enduring nature of the film. As comedy is the most subjective of genres, it is most ingenious to appeal to such a wide variety of viewer mindsets. I believe this to be an unintentional benefit of a decision made for reasons other than audience appeal, but still note worthy.
The unabashed excitement of Ray and the scientific deadpan of Egon may feel unrelatable for the audience, allowing Peter's skepticism to be their way in. He is the everyman, who can be considered a representative of a shared character arc of the Ghostbusters.
At the beginning of the Ghostbusters' journey to self to self sufficiency, dramatically we switch point of view to introduce Dana. As this is directly tied to the main story arc (as seen in the commercial on TV and the forthcoming paranormal occurrence) the tangent avoids becoming a distraction or detraction.
It is traditional if not preferable to displace singular point of view for the sake of establishing the antagonist. This is exactly as done in the first Dana scene with the refrigerator appearance of Zuul. No time is wasted in reconciling the two points of view. After Janine's casual introduction, Dana comes in to converge with the Ghostbusters' storyline.
The origin develops full force in the team's first bust. Their social or relationship must be put to a practical test. This sort of displacement is always rife with comedic potential. (Potential I'd argue is fully and satisfactorily met.)
The montage following the Hotel bust moves us beyond origin and back into the realm of the immediate conflict, but not before introducing an often overlooked side-character.
Winston is a hired hand, a practical man. He can be seen to represent a sliver of the Ghostbuster's relationship with normal folk now that they are an established business. "I've got hundreds of people trying to abuse me!" Winston is the counter point to the general ambivalence and rejection shown by the public.
Winston is also religious. He brings a wider, ontological perspective beyond the specific intricacies of their business, as the trio tend to focus on. He offers this most appropriately in the latter half of the movie, post origin shift to main conflict.
There is another antagonist cut away with Dana and the Terror Dogs, then a point of view change to Louis which is comedic, clearly, but can be justified as establishing sympathy for this side character this is swept into the main conflict. It eases him into prominence.
There are sexual connotations to the "Key Master" / "Gate Keeper" names. It is interesting to note that the mythology depicted in the movie treats human fornication as the only physically transcendental act that can breach the ethereal to allow the antagonist entity into our physical realm. This mythology is sound and widely precedented.
Let's not forget Walter Peck from the Environmental protection agency. His function in the movie is as a single representative of a shared entity, centralized against Venkman. I find this to be a wise move for audience clarity and ease of reception.
Peck vs. Venkman represents the greater issue. They personify the subtle underlying theme: Bureaucracy is rendered helpless in the face of the unknown, and must defer to ingenuity of the individual.
The individual in this case is of course the Ghostbusters. The Bureaucracy, beyond its personification in Peck, is displayed in many forms: the ineptitude of the government AND religion in the face of Gozer's threat. ("I think it's a sign from God, but don't quote me on that.)
When you elevate a character to the fore, as Peter is here, they must also be assigned their own arc to justify this narrative shift of priority. He is, with his personal journey from sarcastic skeptic to sarcastic acceptance, which in turn unifies the Ghostbusters at film's end, linking his character functions in an inextricable way. (Personal/individual and representative/communal.) "See you on the other side Ray." His disposition toward the prospect of Dana's death is especially telling of this attitude change.
You see, Peter's horndoggedness is his way into sincerity. His care for Dana and what happens to her forces him into a change of priority. This aspect of his character plus her place in the story naturally instigate his ascent. His initial unwillingness is overcome. "See you on the other side, Ray."
So Peter functions as both single character with central journey and as a representative of the greater Ghostbusters conflict. This justifies later team-based point of view changes as members disperse. (Egon and possessed Louis, Ray and Winston, Peter and possessed Dana.)
In these sequences it is most evident that comedy is never sacrificed in the face of the paranormal mythology presented. They are constantly intertwined and play off each other, thriving unified. Symbiotic. (ex: Louis's Vince Babble.)
Some may argue that this interpretation is invalid based on the fact that it was not likely the intent of its creators, who were by all accounts focused on making a paranormal adventure comedy. Regardless of intent, a subtle theme and definite character arc are supported by the film in its implications of priority in the conflict depicted. And it is glorious, indeed.