Plot hole: Nile checks the gun Andy gave her and realises it's empty, which in turn leads her to realise that Booker was setting them up, because he gave that gun to Andy in the first place. No way that Nile, a marine, and Andy, a timeless warrior, somehow both missed the noticeable difference in weight between a fully loaded pistol and an empty one.
Suggested correction: That is only true if you handle the same gun all the time. Throughout the movie they shoot dozens of different guns, all with their own loaded/unloaded weights. Different guns are also made of different materials, and mixture of materials, which would change the weight. Different guns are also balanced differently, depending on the materials and manufacturer. The weight difference in a lot of the guns they were carrying between loaded and unloaded were between 3.5oz-7oz (which is not that much). With all the different guns they use and carry throughout the film, it is not a mistake that they wouldn't catch it. Also, Nile is used to carrying an M16 or M4, not the handgun used in the film so she would have no way to know the loaded vs unloaded weight. They would also not expect someone in their team to betray them, so there's no need to check the weapons (although you should check any gun that is handed to you).
Plot hole: The whole premise of the movie is that history would write off the existence of the Ghostbusters after the events of the first movie. In that movie there was prolonged large scale destruction in the heart of a city with millions of inhabitants. It's simply impossible that people would forget or dismiss it. And that's if we do not even begin to assume that the second one happened, even if the director said it did; nothing in his movie shows that, and for a good reason (Statue of Liberty, anyone?).
Suggested correction: There's nothing in the movie to indicate that people in general have "forgotten" or "dismissed" the existence of the Ghostbusters, nor is that the "whole premise" of the movie. The fact the teacher is a fanboy and that the characters literally watch old news-clips and commercials for the Ghostbusters kind of goes against this. People simply just stopped talking about them because they did their jobs too well and went out of business 30 years prior... they were no longer relevant. I mean, if you want a real-world-analogue, just look at 9/11. It was a massive, generation-defining event, and yet outside of brief memorials once a year (which honestly, fewer and fewer people seem to pay attention to every year), people basically don't talk about it at all anymore. The only characters in the movie that don't believe in ghosts/the Ghostbusters at first are the kids. And their mother has been purposely sheltering them because she hates their grandfather-a Ghostbuster. So it makes sense they wouldn't necessarily know about them.
9/11 was a different kind of event; it didn't have 4 easy to remember heroes who already were on magazines covers all over the world and while it certainly dropped off the radar in many ways, some consequences in the long term have been permanent and it is in the history books. Here the world had proof that there are other dimensions, the dead, etc, and years later the Ghostbusters are relegated to a few youtube videos with a few thousand views (that with Peter supposedly teaching advertising and promotion, even). I didn't mention the kids, although the movie itself knows it's absurd that Podcast does not know anything about it and there's a joke about it. I understand if someone makes a point about the movie taking an ample creative license for the sake of not having to deal with 'realistic' implications of its comedic prequels since it wouldn't service the kind of story it wants to tell here, but I am surprised you say that the Ghostbusters here are not forgotten or dismissed. Somehow they are so fringe that not even the conspiracy theory guy knows about them, and the teacher knows because they are a childhood memory.
Like Ray tells a young Jason Reitman in Ghostbusters II, "Well some people have trouble believing in the paranormal." The public would have even less of a reason to believe in or think about the Ghostbusters since there were no Ghost sightings in thirty years. Not to mention the fact that men walked on the moon six times between 1969 and 1972 and astronauts were viewed as heroes, but we haven't visited the moon in fifty years, and astronauts are no longer regarded as heroes.
We keep conducting research in the field sending people in space when and where necessary and people are well aware that astronauts exist, even if they declined in popularity. It's not random obscure knowledge you can get only if you are looking specifically for it on some Youtube channel that a science nut and a conspiration theorist never heard of before. And we are again comparing something that does not have the same impact it would have to learn that dead people still walk (so to speak) the Earth. BTW, I am not sure (but I could be wrong here and please correct me) that the movie says that there have been 'no' ghost sightings at all; Ray said that they received less calls, not enough to pay their bills, not that ghosts disappeared entirely. It's just that in the Ghostbusters universe, people are kinda jaded about everything, which worked when the movies were comedies and you could say it was obvious paradox and satire that they would save the planet and still get sued once they weren't relevant anymore.