It's not a continuity error as such, but I'm a big fan of all the technologies that by rights should have completely upended galactic civilization but then just get forgotten.

The Genesis device should be an appalling superweapon that would change the face of war.

And then those missiles from Generations that can kill an entire solar system should, too.

And the time on TNG that they stumbled on a weird transporter trick that could make it so no one would ever need to die of old age ever again.

And the Tribble blood that cures death.

And so forth.

I'm watching VOY at the moment, and it makes no sense how Seven of Nine's parents would have made contact with and been assimilated by the Borg, decades before Q threw the Enterprise-D across the galaxy to make (what we assumed to be) first contact with them.

In "Q who", meeting the Borg is portrayed like blood in the water — now they have learned of the Federation, they will not stop until you are assimilated. Except oh wait, they did assimilate those three humans several years before, so they would have already known about the Federation.

The 2009 movie. Just, like, the whole thing.

(And I'm not even talking about differences between the JJ-verse and the "prime" timeline; I'm talking about shit not making any damn sense in the internal context of the plot. Kirk was a mutinous fuck-up cadet who should've been thrown out the airlock when Spock had the chance, not promoted straight from cadet to captain by the end of the movie!)

The warp scale changed. The Enterprise exceeded warp 10 several times in the Original Series. Then that infamous episode of Voyager claims that warp 10 is a theoretical limit which is difficult to reach and literally impossible to exceed.

Klingons look very different through the various shows. And more than just costuming progress of the time.

TOS:

TNG-era, the one I think most people would think of:

Discovery:

And the latest show, Academy, reverts back to TNG-era style Klingons.

you mean like new zealand missing in first contact?

So how big are DS9 and the Defiant actually? The scales were all over the place.

The church in Discovery.

I am convinced that they put it there without having an explanation yet, then forgot they did it when they made the explanation.

I enjoyed a couple of seasons of Ben Sisko's heavily-implied-to-be-dead dad.