Babylon 5 set the standard in science fiction for both ongoing narratives and for absolute weirdness. But a good kind of weird. The five year arc of the series was laid out in a very specific manner, following the story of the old races that ruled the galaxy leaving their wars behind and putting the next generation in charge. When you put it that way, it sounds a bit like what the Elves are up to in The Lord of the Rings, something J. Michael Straczynski used for inspiration. Regardless, there were more than a few things in Babylon 5 that never quite added up.
The Size Of The Station
Babylon 5 was the fifth in a series stations meant to be places of peace. The first four stations were either destroyed or mysteriously disappeared, a mystery that gets solved later in the series. But one of the weird things about the show is the scope of Babylon 5. It's an incredibly massive station, so much so that it seems to get bigger to suit the story. That's not necessarily a bad thing but it can be hard to get a handle the actual size of Babylon 5. More than the size, it's the power that comes with it considering it's importance as a massive symbol in the galaxy.
Lorien's Ship
The first of the First Ones, Lorien plays a big role in the war against the Shadows. On the planet of Z'ha'dum, John Sheridan finds Lorien the hard way, by jumping into a pit and dying. Lorien uses his substantial power to resuscitate Sherdian and grant him 2o more years of life.
To return to Babylon 5, Lorien uses a ship to transport both him and Sheridan there. But after they arrive, the ship just leaves, presumably to head back to Z'ha'dum. What happens to it after that is never really explained.
Londo And G'Kar
Londo Mollari is the Centauri ambassador on Babylon 5. G'Kar is the Narn ambassador. The thing about them is these two species hate each other after the Centauri attacked and devastated the Narn homeworld. The animosity is palpable, to the point that Londo has had visions of G'Kar killing him. But by the fifth season, the water is under the bridge and all the hatchets are buried in what feels like a very quick turnaround. G'Kar seems to have forgiven Londo and they are basically friends. While there is some logic to it, the whole situation feels off.
Prophecies
The driving force behind what happens on the show are various prophecies that each species operates under. There are a lot of them, and they hang over the entire series. This isn't necessarily a bad thing but it kind of makes you wonder how the characters don't see things coming.
If Lando knows G'Kar is going to kill him someday, why doesn't he just shoot him in the face and be done with it? There is a lot of inevitability in the series that plays out with such a structured story arc.
Techno-mages
Created by the evil Shadows to be warriors for chaos, the techno-mages used advanced technology to simulate magic. During the course of the series, the techno-mages knew that the Shadows were rising and assembled on Babylon 5 to leave known space. As far as anyone knows, they have yet to return. Why they ran from their masters instead of fighting alongside everyone else remains as big a mystery a why they haven't returned. Essentially, it comes down to fear but still remains an odd choice.
Babylon 5's War On Earth
The Shadows' war against pretty much everything was fought quite literally from the shadows, manipulating everything from behind the scenes. One of their greatest accomplishments was turning EarthGov into a totalitarian regime.
As such, Babylon 5 declares war on Earth to remove the corrupt government and defeat the Shadows. The confusing part is that this is a space station making war on a planet, which the station wins with fewer resources. There are ways to explain this, such as support from the alien races on the station, but an explicit breakdown of the battle is lacking.
Centauri Psychics
Psychics play a huge role in the series. They were created by the Vorlons, a mysterious ancient race that opposes the Shadows. They made alterations to the younger races to give them psychics in the war against their ancient enemies. But one of the younger races they didn't give this gift to was the Centauri, possibly because of their future association with the Shadows. Somehow, the Centauri developed their own psychics, possibly through natural evolutionary means. The why of it all is never fully explained.
Vorlons And Shadows
The ancient races that ruled the galaxy have fought a war going on for centuries, long before any of the other species on Babylon 5 made their way to the stars. Why they are still around is more confusing than anything. The Second Shadow War ends when both the Vorlons and the Shadows leave under Lorien's guidance to move on to the next phase of their existence.
The Shadows basically hung around to be eviler and the Vorlons hung around to stop them, fighting by proxy for a long time. Really, they all could have left centuries earlier and taken their fight with them.
Lennier's Fate
A diplomatic aide to the Minbari ambassador Delenn, Lennier quickly became a fan-favorite character. The end of his run on Babylon 5 was less auspicious than much of his time on the series. His biggest flaw is his secret love for Delenn, but her heart belonged to the commander of the station, John Sheridan. The last time fans see Lennier, he leaves Sheridan for dead in an attempt to woo Delenn. Lennier came to his senses but not before Sheridan saved himself. Lennier disappears after that, reputedly dying off-screen after the end of the series during the Telepath War.
The Telepath War
One of the biggest points of confusion in Babylon 5 is The Telepath War. The event is heavily set up in Babylon 5 and the aftermath is discussed in the follow up series, Crusade, but the actual conflict never comes up on screen. The events are only vaguely discussed without much detail being provided. What actually happens, who is involved and what the casualties were like are all facts left to supposition. There is are novels that fill in some of the gaps but it is still a major event in a very grey area.