My answer is simple.
Consistency
You are welcome to invent any rules you like. But, once invented, you need to hold to those rules, or have plausible exceptions to those rules that make the audience feel SMART for having never considered them (or having considered them, but been validated later on).
So... things that don't really bother me... Gas tanks that explode or start fires when shot (this doesn't happen in real life). It's more exciting when things blow up, and it allows you to do cooler stuff with action scenes. Alien languages translated without explanation. It doesn't bother me as it means I just get to understand what's going on much easier. Stuff of that nature. "Rule of Cool". Things that ultimately ramp up the "fun" without really being consequential to the plot at all.
Things that do bother me...
1. What are the freakin' limits on a Replicator in Star Trek? Can't they just replicate some money anytime they need some? Why not? Why don't they? What about any random want? Why don't they replicate booze? Or other illegal drugs? Why do criminals steal things when they can just replicate them?
2. Why can't they fly the giant eagles to Mordor to drop the ring? Actually... why do they have to drop it in THAT PARTICULAR volcano? Aren't all volcanos linked to the same overall magma across the whole world? Couldn't they pick a volcano in the opposite direction? Why not? Couldn't they have created their own lava with magic to destroy it?
3. Why does a person wearing glasses have to automatically be a smart nerdy scientist... or a hopeless loser? Glasses do not add +20 to INT.
4. Houses in video games with not enough beds/chairs/rooms for the amount of people who live there. It is seriously immersion breaking when you realize a family has one bed... and 10 children. It's squicky as well.
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Basically, I need a base minimum effort put into the game/movie/book to provide explanations for things. Limits.
For example... in Science Fiction... they often have "Gravity Manipulators" to provide enough gravity to be on starships. But, their weapons are all lasers and such. I'm sorry, this makes no sense. The most dangerous thing any race could ever get hold of, is the ability to manipulate gravity. The crazy, terrifying, and horrifying things that can be done with such a power... Especially when the generator for it could fit into a ship no larger than a 10 bedroom home... Imagine just ripping chunks out of other ships with it. Or, using it to force objects into each other. Imagine using it to destroy the bonds between atoms and crumble people into their base elements. Imagine using it to shatter planets or kill stars. Imagine using it to immobilize criminals via a gun and lifting them into the air via gravity field.
Do you see what I mean here? When you introduce something insanely profound with hundreds of millions of baseline applications... You need to explain the limits, why it isn't used more often, why all current technology doesn't use it, etcetera.
Mass Effect 1 did this very well and their "Mass Effect" fields. The moment it was discovered, they used it for practically everything. They put it into their GUNS to make them fire faster than the speed of light. This is how you do gravity/inertia manipulation tech.
Other games do similar things with their magic systems. They don't really explain them or establish rules with them. They just slam new magic powers into the plot when they need something "unexplained" to happen.
I'm sorry, but when you have something that obviously affects the entire world it exists in... you need to spend some time addressing pretty much every possible angle of it. Because, if your audience thought of something they could do with that magic or that tech... Guaranteed, someone who had to interact with that magic or tech on a daily basis in the world you've created, would've thought of it first. There would've been consequences for what it was as well.
I need internal logic and consistency. I need you to have thought of everything when introducing me to something. To have 400 pages of backstory and explanation somewhere in your design document about it. Because, you are building a world. Because you need to be able to apply your rules across the board and make sure it's consistent.
I don't mind if you have very little "realism". I mind when you just assume I know how something works, or should work. I mind when you assume I won't ask questions. I mind when you assume I'll just roll with it and not consider 30 other ways to end your plot using YOUR OWN RULES FOR YOUR SETTING AND STORY that you didn't even bother considering.
Do you know what REALLY kills immersion for me?
When the only way your plot works is if the collective IQ of the entire cast of your story or setting is about 18. Namely, if the only way your story works is that everyone is a freakin' idiot and doesn't bother clarifying things, explaining things, apologizing for things, or just avoiding stupid actions... I check out. I can't do it. Real people do not act that way. Yes, real people do stupid things. Yes, they prolong their own problems for a variety of reasons. But, most people have some sort of motivation for doing so. They don't do it because it's what "fate" expects them to do, in order to move things along.
If the plot of your story (or the JRPG) can be solved in about 10 minutes if everyone just grew a brain... it's a bad story or bad JRPG that I just refuse to play.
Immersion broken.