In the end of the 1st episode Professor Arturo cited Lenin's full name as "Lenin. Nikolai Ilyich Ulyanov-Lenin". Lenin's name in real life was Vladimir Ilyich. According to the plot, Arthuro knows history well, and he wouldn't make such a mistake in the name of one of the most famous politicians of the 20th Century. The homeworld of the Sliders is not our real life one, so it would seem that on the show's "Earth-Prime", Lenin's given name was different.
At first the Kromaggs would seem to be historically wrong, since the Cro Magnon Man on which the sliders speculate they are descended from were the first "modern humans" - but that's on OUR Earth Prime. That means that the Sliders are actually further from our modern human species than the Kromaggs are! In short, WE are the Kromaggs (or at least are a close parallel)
For all the debate about which Arturo slid, the series left one clue that resides in this trope. In Season 3's "The Guardian," Arturo says he has just seen his first American football game, but in Season 1's "Summer of Love," Arturo knew the context of "wish-bone" and seemed very familiar with the sport in general. Both episodes were written by Tracy Tormé, who whenever asked about this, would reply along the lines with "Maybe you're on to something." In 2009, Tormé stopped implying and outright said that it was the alt-Arturo who ended up with the Sliders.
It's almost certainly unintentional, but the two Arturo's attitude to American football fits their respective characters well. Original "good" Arturo would be more likely to take an open-minded interest in the sport upon coming to America, whereas his nastier, more elitist double would probably disdain the American sport.
Theres actually arent any major plot holes in terms of the Kromaggs. The Kromaggs of Invasion dont appear to have encountered humans before they started sliding (which they did for at least a generation). In The Other Slide of Darkness alternate Quinn reveals that he gave the Kromaggs sliding technology. From that point on, all the Kromaggs encountered originated from a world which they shared with humans (and where sliding technology existed at least since Quinn was a baby). The only assumption needed to make this consistent (and one which makes perfect sense in the context of the show) is that there are at least four different worlds that gave rise to the Kromaggs (as opposed to the hundreds of worlds which gave rise to humans). This means there are really four types of Kromagg (at least). There are the ones from Invasion, the ones alternate Quinn gave sliding technology to, the ones from Quinns homeworld and the ones from Revelations (the good Kromaggs who were explicitly shown to be different from the main Kromaggs in the series). This also falls under fridge horror since it implies that, while the Invasion Kromaggs conquered 150 worlds, thats only a subset of all the worlds the different types of Kromaggs had conquered in total.
A minor one in Eggheads. One of the books the library rappers pull of the bookshelf is by Chekhov. Then at the end of the episode when the sliders are being chased by the mob, they escape thanks to someone moving a bookshelf into the way of the pursuers... er... Chekhov's Bookshelf?
In "Paradise Lost" (which is a rip-off of Tremors), the mutated monster leaves behind a trail of blue slime wherever it goes. The locals don't try to kill it because its slime can prevent aging and prolong life. How is this Fridge Horror? The slime only works this way if you eat it.
In "Gillian of Spirits," Quinn is trapped on the astral plane and can only be seen and heard by the titular Gillian. She has a history of hearing voices and many (including Gillian herself) think she's crazy. And the voices did eventually go away. However, given Quinn's predicament, perhaps those voices weren't merely in Gillian's head. Perhaps they were other Sliders, who unlike Quinn, weren't as fortunate to escape the astral plane alive.
In "The Other Slide of Darkness," Maggie comments that she was never much of a team player. The sentiment is echoed in "This Slide of Paradise," where she says she didn't learn to be a team player until joining up with the Sliders. Of course, before joining up with the Sliders, she was in the military for years. Maybe not being a team player is the real reason why she went from fighter pilot to intelligence officer.
In "A Thousand Deaths," Rembrandt and Mallory take part in the Arcade, a place with sophisticated, realistic video games. Later, you learn the Arcade's big secret - the video game characters aren't mere holograms, but real people hooked up to the system. Everything done to them is real and after a thousand deaths in-game, they die for real. One game mentioned but not seen is a hospital game, where a player gets to be the doctor in emergency room surgery. On a world that seems to run on Video Game Cruelty Potential, think about that for a second.
In "Summer of Love," the Sliders barely escape an incoming swarm of the dreaded spider-wasps. However, right after Quinn and Arturo emerge from the vortex onto the next world, several spider-wasps are shown flying right out. So few probably wouldn't have the same effect as on the previous world, but they would still be enough to cause significant damage. More so if one happened to be "queen" potential!
It was never explained whether they reproduced like spiders or wasps. In either case, only three got through, one of which was crushed by Arturo. There's only a 50% chance they were the same gender; even if they were, and these things reproduce like spiders, they would have had to find each other again and not get killed in the meantime. AND, with such a small gene pool, it's quite possible some recessive gene will kill all of them - especially likely since they were genetically engineered rather crudely. However, if all those things go wrong, yeah, things are going to get very unpleasant in that universe shortly later.
On re-watching, the original swarm was started when a queen escaped. Just one. Eep!
In "Summer of Love," the American president is said to be Oliver North. The later "Exodus" two-parter also has Oliver North as president. While possible a coincidence, fans have suggested that both storylines featured the same parallel Earth. If true, then all those people the Sliders befriended in the former wound up dead in the latter.
The worlds seemed to have some other similarities. Maggie once mentioned that the Pacific War with Japan lasted longer in her world, as did the Cold War. While the specifics mentioned weren't the same, this corresponds to the world of "Summer of Love" which was stuck in the Cold War 60s.
In "The Weaker Sex", everything the Sliders were about to accomplish is undone by an ill-timed slide. But if you think about it, their intervention must have left things far, far worse than before.
This could not be more wrong. Think about this: Arturo's the first man to run for mayor, and there's a history of violence against him (e.g. people throwing bricks into his campaign offices). Just after he gets elected, he completely disappears off the face of the Earth. That he was murdered by someone who didn't want men to gain power would be a very logical conclusion, and that would make him a martyr, increasing support for the cause of gender equality.
Colin's fate, to be "unstuck," that is, bouncing around dimensions "for the rest of his life." Eesh...
OK bear with me on this one. It seems that the vast majority of Earths they visit (and thus presumably the jillions of ones they don't visit) are pretty much identical to our Earth except for some - usually relatively recent - details in human history. e.g. Women are the dominant sex, variations in cultural norms / traditions / politics / etc. So it's reasonable to assume that really only living things have an affect on the differences between worlds. e.g. they never slide into a universe, where, say the Earth never formed, or its orbit is too different from ours to support life despite it being overwhelmingly likely all things being random - in fact in many worlds, copies of the sliders themselves exist. So the more major events in the entire universe (other than the histories of living beings) would be pretty much identical in all universes, except the very odd example, e.g. that world where time ran backwards - but given the rest of the series, I think that's an unusual case. I'm getting to a point here ;) If the orbit of Earth is the same in every universe it implies that the orbits of all planets, stars, celestial bodies etc. would be the same. This means that the world in which a comet was on a collision course with Earth was not only not unique, but probably happened on nearly every single Earth in existence! That particular Earth was lucky enough to have Arturo & co. help destroy it with a nuclear missile, but think about how many Earths must have been wiped out by comets where nuclear missiles were not readily available!
It is actually stated in "Net Worth" that the vortex will only open in an atmosphere so the idea that "they never slide into a universe, where, say the Earth never formed, or its orbit is too different from ours to support life" would never happen. Meaning cosmic events can also affect world formation.
There was also the world that was completely on fire, but luckily they were only there for like ten seconds (good job the timer didn't drop them there for a week or so!). No explanation is given for this world.