These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Big Lipped Alligator Moment: The dream sequence in the first film, remnant of a cut scene that appears in its entirety in the novelization. The entire footage of the original scene, and others that were cut through production, has yet to ever be released.
Cult Classic: The first film has a strong cult appeal, although unlike most cult classics it was massively successful and beloved on its release, too. The second probably counts as well; it's just not as loved as the original.
Ear Worm: If there's some damn song / runnin' through your head / who ya gonna call?
Genius Bonus: In the first film, Venkman asks the librarian if there's any history of mental illness in her family, she mentions that she had an uncle who thought he was St. Jerome. St. Jerome is the patron saint of librarians.
Harsher in Hindsight: The first movie's scene in which Venkman tries to "scientifically" disprove the first ghost's existence. He asks the librarian if she has a family history of substance abuse… accusations of which later destroyed Bill Murray's second marriage.
Also in the first film, when the containment system is shut down, the trapped ghosts are released throughout New York and see them flying out over Manhattan. During a long-distance shot, they seem to originate from right around the Twin Towers. So we have bright lights and ghosts flying out from the World Trade Center towers. One of the memorials to the Twin Towers has been shining twin spotlights straight up into the sky from Ground Zero once a year.
Hilarious in Hindsight: Peter MacNicol (Janosz Poha) would later play an art curator who was forced to host Mr. Bean. Harris Yulin (the judge from the second film) was the owner of the museum!
It's the Same, Now It Sucks: One of the key points of criticism about the second movie is that it's in many ways a repeat of the first.
The Stop-Motion terror dog in the first movie just doesn't look like it's actually there, even though they do a fairly good job of having it crush a table and smash down a door. The puppets, however, are very well done.
Towards the end of the first movie, a rather large rock harmlessly bounces off of a police barricade instead of crushing it.
In the widescreen version of the first film when the ghosts escape, there's several incomplete ghost trails.
In Ghostbusters II, the mechanism that makes the toaster dance is clearly visible.
Strawman Has a Point: Walter Peck's initial request to see the containment grid was reasonable. He's also quite polite before Venkman gives him the runaround (albeit in a rather unctuous and condescending manner). It is his job to make sure people like the Ghostbusters are operating with safe equipment, and in fact the Ghostbusters' containment grid could cause a massive explosion in a densely-populated area. In fact, Egon was at that moment telling Ray and Winston that he was getting worried at the massive amount of psychic energy the grid was containing. After getting crudely brushed off by Venkman, however, Peck overreacts and orders the grid's immediate deactivation. If Venkman had cooperated, instead of treating Peck and the EPA as an enemy from the start, they could have avoided the ensuing meltdown.
Walter Peck: Forget it, Venkman. You had your chance to co-opperate, but you though it would be more fun to insult me. Now, it's my turn, wiseass.
This was probably intentional on the part of the writers, though. A deleted scene shows that the reason the Ghostbusters got kicked out of Columbia was because Venkman was the one representing them at department meetings.
Of course, given the atypical and experimental nature of the Ghostbusters' technology, it's highly unlikely that a career bureaucrat like Peck could even understand what he was being shown; the technician he brings to deactivate their equipment actually realizes this, and desperately tries to warn his superior of the danger before Just Following Orders and triggering a near-apocalypse. Giving in to Peck would have just made it all happen sooner, possibly even in a manner in which Peck could have kept the Ghostbusters from stopping Gozer.
The Problem with Licensed Games: The 2009 game was critically acclaimed, and the 1990 Sega Genesis game is regarded to be pretty decent, but other than that the games based on the series haven't fared too well. In particular, the 1980s game by Activision based on the first film tends to be regarded as interesting in concept and scope, but extremely tedious in execution (and the NES port of that game flat-out horrible).
Unfortunate Implications: Only in a Japanese Ghostbusters pachinko game released there: While the game use footage from the movies, for some reason, they eliminated all the footage when Winston appears on-screen, leaving only Peter, Egon and Ray as the only members in that game.
Pretty much the case in many other manifestations of the franchise other than the animated series (like the role-playing game directly based from the movie); you hardly get to see poor Winston in them.
Visual Effects of Awesome: The films have aged very gracefully over the years. The proton pack streams in particular look about as good now as they would with modern CGI effects. And not to forget Stay Puft. The only thing that has dated somewhat is the stop-motion of the terror dogs, but they are still scary.