In "The Last Train to Oblivion", the ghost of Casey Jones was able to pass on after managing to prevent a train crash. Now, there was no danger of a train crash until Casey kidnapped Peter and started the stolen train down the tracks in the first place... but the problem wasn't that he had to avert a crash. It was that he had to perform his legendary, spectacular run, pushing the engine beyond the limit, doing what was thought to be impossible... AND not crash. It wasn't penance; it was post-mortem OCD.
In "No One Comes to Lupusville" the boys visit a town full of vampires and werewolves. Three dozen episodes later they're hired by a Boldavian count who claims to be the last vampire, and no one gainsays him. Guess we know who ultimately won the battle in Lupusville ...
To be fair, we do see more vampires later in the series. So the count is basically just being emo.
Or he's just the last vampire in Boldavia.
In "Three Men and an Egon," upon returning to his adult self, Egon is asked if he really doesn't remember what just happened to him. He doesn't... because humans don't start really forming memories until they're anywhere between 3 and 5 years old, and Egon spends the majority of the episode as a baby that's probably barely a year old, if that.
In the episode "Janine, You've Changed" it's hinted that Janine's "Fairy Godmother" haunted Cleopatra and Marilyn Monroe. What did these women have in common? Both were praised for their beauty to the point that their intellect was overlooked. Both look different in various images of them. (The RL explanation being plastic surgery and bleached hair for Marilyn and artistic interpretation for Cleo.) Both women are believed to have committed suicide.
It's also hinted that the "Fairy Godmother" haunted a woman of the Tudor era. Which one? Possibly Anne Boleyn. It was her youthful looks that drew Henry VIII away from his first wife and she may have felt pressure to stay beautiful to keep him interested. One of the charges against Anne Boleyn when she was sentenced to death was witchcraft. If she was seen talking to a shade and then changing appearance, that would be seen as witchcraft.
In "Night Game", we're told that the spirits of good and evil are battling for one human soul. We later learn that said soul was Peter's. Interestingly enough, part of the battle may have been taking place off the field. The Referee had told the Ghostbusters that no one could be neutral, and that Evil cheats, but Good must never do so. Egon realizes that if they use their proton packs to zap the Evil pitcher, they'd be cheating, and thus siding with Evil. But who was it that proposed the plan? Peter. The battle was decided when Peter was convinced to have faith in Winston's ability to hit the fiery fastball, instead of cheating to win the game.
In one episode, Winston asks Egon if he can read Sumerian. Egon replies, "In my sleep. Underwater, and with the lights off." This comes off as a bit of hyperbole, until you remember that Sumerian was cuneiform carved into tablets, and would have a texture. And knowing Egon, it wouldn't be outside the realm of possibility for him to have learned to feel Sumerian script in much the same way as one feels Braille. More brilliance comes from remembering that the team's Archenemy Gozer hails from Sumeria and most of the primary sources on that entity would be in that language.
In "The Joke's on Ray", Egon serves Ray, Peter, Winston, and Slimer sandwiches, and they enjoy them until Egon reveals that he made them to provide the nutrients lost through sweating. They take this to mean that the sandwiches are made from "synthetic sweat", however, the nutrients lost in sweat are mainly potassium, calcium, and magnesium — all of which are found in many foods. This explains why Egon's friends enjoyed the sandwiches initially; they were probably actually made with normal ingredients.
In "Doctor, Doctor", Janine states that chicken soup is Egon's favourite food. Egon is Ambiguously Jewish, and some chicken soups have had significance in Jewish culture.
In the first episode, "Ghosts R Us", the Class 10 runs over a bunch of cars using its bike. What's disturbing is that we only see one car have its passengers safely get out before getting destroyed. Did this entity just kill dozens of innocent people before it was destroyed?
J. Michael Straczynski explicitly notes this on the commentary for that episode, saying that the network never let that happen again.
In "The Cabinet of Calamari," when the disappearing victim escapes from the cabinet, he asks for some money to call his wife. Winston informs him that since he's been gone, the cost of payphones has increased. The man was in there for years without aging or noticing the passage of time, and chances are his wife has aged or moved on without him.
In "Buster the Ghost," the titular ghost decides to kill himself after yet another failure at a job, this time as a tooth fairy. As he says this, he makes a Finger Gun gesture pointing at his head. As shown in other episodes, ghosts can shot with their hands in that gesture. It may have been possible that he really was going to commit suicide within a few seconds if he hadn't been interrupted by his talking watch.
In "You Can't Take It With You," after the team break into the mansion of an insane millionaire teleporting his money into the Spirit World so he can keep it after he dies, they find and release three of his employees. The prisoners say their boss "was going to put us in that terrible machine" after he finished with his fortune, but given that: the guy is old, frail, and gets around via motorized wheelchair, and had no way of forcing them into his machine; the building was otherwise empty, as is stated outright later; they were locked in an airtight room; and Egon explicitly finds the plan "very Egyptian," it seems more likely he was planning on sending them to the afterlife the old-fashioned way...
If "The Thing In Mrs. Faversham's Attic" was trapped up there for 70 years, why did it only start bothering Mrs. Faversham enough now to seek the Ghostbusters for help? Remember that Mrs. Faversham, and then the Ghostbusters, heard its rumbling and laughter before they got anywhere near the attic. That suggests that the Thing was already starting to break out of its prison. Given that Charles Faversham was so horrified at what he'd summoned that he renounced it and imprisoned it in the attic, it's probably for the best that we never find out what it would have actually done if it had freed itself.
The more feminine, mild-mannered Janine with the long straight hair, rounder glasses and softer, less regional voice from the Lighter and Softer season 3 forward - with a few other makeovers along the way - becomes incredibly disturbing after you see "Janine, You've Changed" and realize that she was secretly being manipulated and physically altered by a demon all along. By extension, pretty much all the Lighter and Softer episodes become a lot more disturbing when you realize what was happening with Janine and the demon.
What's worse is that the demon was also manipulating the consciousness of the Ghostbusters, and Slimer, so they wouldn't notice the changes. If Slimer hadn't found an original photo of Janine, by sheer chance, Janine could well have been lost forever, and who knows what the Demon would have done then.
This is perhaps made even worse considering that an Egon/Janine relationship was not allowed because Harold Ramis did not approve, yet the writers kept the idea in as a one-sided crush. What started out as a character trait eventually developed into a situation where Janine was so hopelessly in love that it became an obsession that almost led to her own death. Had the writers simply abandoned the one-sided crush early on, this never would have happened. The worst part was that the crush was often played up for comedic effect early on. Extreme Ghostbusters later had Janine outright state that she has low self-esteem and doesn't see herself as very attractive, and actually believes a man asking her out on a date is insincere (he actually was sincere—he turned out to be a demonic insect that wanted Janine as his queen but it was still a sincere attraction). What little we see in the series though suggests either Janine is asked out yet turns down men due to this, or in fact no one does flirt with her for some reason. Her obsession with Egon may be due to human nature to develop a strong desire for things we can not have, which worsened over time and allowed a demon to use her.
The Containment Unit. It's a massive disaster waiting to happen. Any time it is shut down, the collection of horrible things, including ghosts, eldritch abominations, demons, and other assorted terrors, are moments from escape. Now, consider, the Ghostbusters won't be in business forever. They've almost put themselves out of business on numerous occasions. And even if you can count on newer ghosts and demons showing up, the Ghostbusters can't keep doing it forever. Even with Extreme Ghostbusters, you have to consider that at some point or another, there just might not be any replacement Ghostbusters. So what happens then? Does the cost and maintenance of the Containment Unit fall on the taxpayers? What if it goes forgotten, and the power shuts down? It would be akin to another 9/11 or a nuclear blast.
In the episode "Bustman's Holiday", Ray tells the townsfolk to bury the garbage trucks functioning as makeshift traps, and give the ghosts time to "deres". These ghosts are explicitly the souls of deceased people. That means that the effects of a trap on a soul over long terms has a degrading quality. Still want to call the Ghostbusters to capture the annoying ghost of a late relative living in the haunted house?
Several members of the Ghostbusters staff have been possessed or had their souls removed from their bodies over a period of time. One wonders if they need counseling afterwards for the feelings of violation and Mind Rape that must surely come from having an Eldritch Abomination inhabiting your body.
As expensive as the Ghostbusters' services are, they're just barely meeting their expenses while in operation. Facing a "dry spell" of less than a month, had them on the brink of bankruptcy. If Peter hadn't managed to catch a bank-robber with a four figure bounty, they would have been foreclosed. Think about that for a moment.
In "X-Mas Marks the Spot," capturing the three Ghosts of Christmas leads to Scrooge winning and Christmas being ruined—and also means that Tiny Tim died, among other things. Worse, Jacob Marley wasn't caught. Given his role and punishment, he would have seen exactly what kind of misery an unrepentant Scrooge caused and likely blamed himself for not getting through to him.
In the episode "Knock Knock", the premature opening of the doomsday door causes dark forces to escape and causing chaos. Including causing a subway train to come alive and go wild... we see people terrified in it as it flies off. The Ghostbusters board the same train later in the episode, and it's empty... then it blacks out for a moment, then it's filled with skeletons wearing modern clothes who all slowly turn towards them, laughing with hands out-stretched.
In "Chicken, He Clucked" a paranoid man resorts to using dangerous magic books to summon a demon in order to rid the world of the chickens he hates so much. Poor guy had never gotten the help he needed - much like people with mental disorders in real life - and when he is finally admitted to a mental hospital, he gets abused (albeit not by the inmates or the staff), which is often Truth in Television.
The Sandman genuinely wants to protect humanity from itself, but what would happen if a natural disaster occurred while everyone was asleep? The answer? Countless innocents could be injured or killed, and no one would be in a position to come to their aid. And if he put all the Ghostbusters to sleep, no one would be left to stop later paranormal attacks. And if their bodies were still functioning while they were asleep, as opposed to being in suspended animation, everyone could have either starved to death or died of dehydration.
In "Adventures in Slime and Space", the giant Slimer grabs Janine for no apparent reason. Was he planning on eating her?
