God Test: Have gone rather out of fashion since most examples of a miracle became something people could purchase at their local hardware store, leaving things people could ask to be done as proof of divine bona fides too academic (“Violate conservation of energy!”), too insane (“So make a rock too heavy for you to lift, then lift it anyway!”), or impractically large (“Go ahead then, CREATE A UNIVERSE.”).
A Glitch in the Matrix: Avoiding this sort of thing, when it comes to virtual reality, is one of the few legitimate uses for the Out-of-Mind visual textures. (Others mostly including hiding gifts and playing really terrible practical jokes.)
A more commonly seen variant are “weavespiders”, small metallic fractal spiders (which everyone knows to ignore) used in virtual realms to collect trash, reassemble broken scenery, and otherwise do maintenance. While, obviously enough, this can simply be done programmatically without requiring any visual metaphor, reifying them like this is a simple way of avoiding the uncanny valley effect of changes “just happening” with no apparent in-world cause.
Giving Radio to the Romans: Tends to happen quite a bit, given the lack of any Prime Directive-equivalent and the large number of free traders around who are more than happy to sell anything to anyone who can pay – and that’s not even counting the “fell off the back of a starship, guv, ten bob to you for cash” crowd – and the desires of most people on most worlds for shiny toys.
Some of the real life consequences mentioned are prevented by the Empire’s also having a bunch of private organizations of various kinds, including professional civilization-uplift consultants, who go around helping people not to be total screwups under these sorts of circumstances… but not all of them. But, y’know, free will and all, and it’s not as if they made you invest in technologies granting you the capacity to be total dicks and then use it in that exact manner, belike. That’s on you.
Geometric Magic: Well, not magic, no. But a lot of the Flamic rites and rituals make use of sacred geometry, as reflecting the perfect order of the conceptual universe. Elmiríën, in particular, as eikone of order, structure, stability, perfection, and proper functioning is very fond of these, to the point of self-representing as a perfect orrery of Platonic solids.
Also, there’s a lot of geometric engineering.
Genius Breeding Act: Averted, despite the tremendous respect for intelligence – as you might expect from the civilization that considers Arranged Marriages an unpleasant subclass of slavery. (Which, as I said back then, doesn’t mean that friends and relatives aren’t happy to engage in generous quantities of Shipper on Deck…)
…actually, more inverted, in a sense. The Reproductive Statutes do do the opposite, since while fully recognizing the rights, etc., of those with hereditary disabilities, since ethics is time-directional, that does not extend to deliberately or negligently creating more of them, respecting the right of the potential sophont to be well-created. And for a sufficiently advanced society, “hereditary disabilities” includes “functional amentia” to a degree that goes a long way farther than anything anyone in our history would have classed as even mild intellectual disability or other related conditions.
So if your genes aren’t up to scratch in this area, no reproduction for you! That’d be felony dysgenesis.
Gem Heart: Truth in television where silicon-based or carbosilicate lifeforms are concerned, although while some make use of gem-like structures (say, the galari, who even look like cut gems due to their crystalline structure) one is equally, or even more likely, to find Rock Heart. Or plain old crystalplasm.
Otherwise, mostly seen as things like the trope-page-mentioned gizzard stones.
The Game Come To Life: Doesn’t happen literally, but perhaps a little played with inasmuch as there are augmentality games – designed to integrate seamlessly with the real world and make use of real-world elements during gameplay – which blur the boundary more than a little. (Enough so that a number of them have been manipulated by various sponsoring entities to achieve real-world goals. Amazing what people will do for progress towards an achievement…)
And then, of course, there was the Lord Blackfall incident.