Right after the storage grid fails and blows out, as the Ghostbusters, Peck, and police are having a scuffle, you can see firefighters are beginning an attack on the building. As far as they know and have been told, they're looking at a structural fire. While we're not told anything happened to any of them, that sounds like pure luck - running into a building with that many recently-freed and likely highly pissed, dangerous ghosts must have been insanely dangerous, particularly given the only thing Egon can think to yell during the failure is a panicked "Clear the building!"
The hotel manager’s situation when he calls the Ghostbusters to deal with Slimer. Yes, there’s the stereotype of a high class hotel trying to deal with a problem while pretending that it doesn’t exist, but it’s very clear that this guy knows exactly how real the ghost responsible for the disturbances is, and is possibly afraid that he will be seen as a nutcase if he makes this claim to the complaining guests. Just imagine what it would be like to suffer the presence of a mischievous or malevolent spirit, knowing that most people would dismiss you as insane if you told them the truth.
If the hotel maid hadn't been standing behind her cleaning cart, she could have been killed because the guys got jumpy with their proton packs.
Scientific experiments usually require a control subject. In Venkman's experiment, the pretty co-ed is pulling triple duty as the control subject, a vessel to manipulate the actual test subject, and a possible date for later. Venkman shows his willingness to again combine work with pleasure when dealing with Dana.
Pay attention to the flash cards Venkman is showing. While the young man keeps getting them wrong (until the last one), his answers always predict the next symbol that will be shown. He doesn't have ESP, he has precognition!
Now consider what Venkman is studying with this experiment: "The effect of negative reinforcement on psychic abilities." After repeated shocks, the test subject actually names the card in Venkman's hand, rather than the next card to be drawn. Venkman might, in fact, be on to something with his theory!
Egon's warning against Crossing The Streams makes sense when you think about what those devices are: focused proton emitters (like a laser, but with sub-atomic matter instead of light). Protons are positively charged. Particles with like charges repel each other. Two or more proton streams colliding is likely going to cause a massive repulsion effect, setting off nuclear chain reactions around the immediate vicinity (depending on the relative atomic stabilities of the surrounding objects). Not pretty.
Watch Zuul and Vinz Clortho during the final confrontation with Gozer. They continue to exhibit the same behavior that they did when possessing Dana and Louis, respectively. Zuul is calm and business-like, even intently staring at Venkman after her transformation, clearly recognizing him. On the other hand, Vinz is fidgeting nervously on his stone slab and is the only one to get stroked like a puppy by Gozer. He even tilts his head in a puppy-like fashion when the Ghostbusters get zapped by Gozer.
In her apartment, early in the film, Dana compares Venkman to a Gameshow Host. In the original script, she was supposed to compare him to a used car salesman, but this was improvised by Sigourney Weaver into the line that we know today. If you look at Venkman's character development throughout the movie, he actually turns from a used car salesman into a Gameshow Host— shedding off his deception and cynicism in return for genuine enjoyment of the situation that he's in. Instead of conning people into doing what he wants, he's now using his personality to wrangle them into participating in the fun. Of course, this line is also given a loose Call-Back in the second film, when Venkman is shown to have actually become a paranormal television show host.
If you look closely at the "magnificent feast" that the group is eating just before their first real call, Egon is drinking soda, while the others have beer. Seems odd, until you realize that they're still "on call," and if they need to drive out (which they do), one of them needs to be sober. Egon is also established to have a major sweet tooth, so likely he prefers sweet soda to bitter beer, making the choice of him as the designated driver an easy one. The Coca-Cola Product Placement also helps.
Vinz says that Gozer will appear in one of its pre-chosen forms. The guys are surprised that Gozer initially looks like a naked woman. Just like Ray, someone before them must have tried to think of as harmless a shape as possible, possibly even a former lover.
Peter is initially dismissive and mocking of Ray and Egon's assertions about ghosts being real. At first this would look like him being a fraud, but then recall that his degree and field of study is in parapsychology... the study of the unknown or paranormal parts of the human mind and behavior. He's essentially only grouped with Ray and Egon in their studies of ghosts because the university put them all in the same "weirdo" department.
Louis's borderline stalking of Dana is more understandable and sympathetic if he was literally destined to be the Keymaster to her Gatekeeper, especially with the massive rise in spiritual energy in the city as the ceremony neared. The fact that he switches his romantic attention to Janine in the sequel supports this idea.
When the Ghostbusters wake up after the Stay-Puft Marshmallow Man's explosion made them pass out, the first one to awaken is Ray. This make sense, since he's the most energetic of the boys.
Dana isn't just watching the Ghostbusters' rise to fame because it's sweeping the media. She's probably relieved as all hell to find that the group of weirdoes that she went to for help seem to be legit, and that others are having problems like hers, and the Ghostbusters are handling them.
