These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
If you let the Psilons develop unopposed, they *will* climb the tech tree. This is usually followed, at some point, by them climbing all over you, guns a-blazing.
In the original game, Silicoids, especially in smaller galaxies. They could colonize any planet right from the start, meaning that in small-size galaxies they could literally take over half the galaxy before the other races got the technology to colonize (or invade) planets with bad environments. And of course more planets = more population = more industry = more research = better ships.
Fanon Discontinuity: The third game. This included a LOT of backstory that had never been hinted at in the previous games and never mattered in this entry either.
There's also the "Orion Globe" design in MoO2, a Death Star-sized battleship that forgoes the typical Stellar Converter for a combination of scanning equipment and refined weaponry that allows it to sheer through all forms of shields, armour and defences, wiping out whole fleets in a number of turns.
The Psilons in MoO 2, if AI controlled. They have huge bonuses to scientific research speed, and gain automatic access to every technology in the game rather than having to pick and choose useful techs from a catalogue of options based on the situations they encounter. As a result, by the middle of a long game an unmolested Psilon empire can expect to be unambiguously more powerful than any rival empire, and by late in that same game, the Psilons can expect to have grown so overwhelmingly powerful that they can effortlessly defeat even alliances of all their rivals.
The Antarans. Seriously, you'll be watching over your empire, minding your own business. Next thing you know, the music changes to an ominous tune, and Space-Cthulhu is in your face, giving you a heads up before ravaging a colony.
The space amoeba. Sure, it looks stupid and most of the time its just harmlessly floating around impeding your attempts to colonize other planets. But then they actually attack. Big whup, what permanent damage could they... oh god, they ATE the PLANET?! Whole?!
Sequel Phobic: The designers of MoO 3 were emphatic that they were making "Master of Orion 3, not Master of Orion 2.5." In retrospect, MoO 2.5 may possibly have been a lot better.
Serial Numbers Filed Off: The mobile game Starbase Orion is essentially MoO 2 with a fresh (and thin) coat of paint. Not that anyone is complaining.
That One Boss: The Crystal Life Form from the first game, sort of. Triggered by a random event, it could appear anywhere and anytime. If you didn't have a big, heavily armed fleet of Large or Huge ships armed with not-missiles? Hope it doesn't approach your territory. Or appear right inside it.
They Wasted a Perfectly Good Plot: The backstory added in 3 is actually pretty good, and includes a number of good ideas and motivations for the various races as well as a major universal foe that the Antarans themselves are terrified of. Pity the actual game totally ignored it beyond a few leader characters.