Often when LN readers complain about the anime adaptation skipping stuff, it's not as bad as they're making it out to be.
However, as an anime only, in the case of Unnamed Memory, they are 100% right. At least, I hope for the LN's sake, that this anime is skipping a lot.

To briefly touch on aspects other than the story and characters, visually and audibly, the anime was fine. The music was fine. The OP was good in particular. Animation was serviceable as wel. Not great, not bad. Actually very little CG. Props to that.

For the rest: I will use spoilers, but to give you my score up front: 35/100. It's awful. Poor character development, poor world building, poor pacing, skipping important information etc.

The anime starts off fine. Nothing ground breaking, but it's nice. Prince Oscar meets Witch Tinasha and Tinasha goes with Oscar as a kind of bodyguard to cure his curse. Then, halfway through, the cracks start to show. You start to notice that you are missing crucial information, world building or character development that probably should've happened in the first half as character motivations and plotpoints start to not make sense anymore.
For example, you're being told the world hates witches and magic, but are shown the opposite. Only being shown the supposed hatred by the ones you're supposed to dislike and when it's convenient for the plot. Yet a large part of the plot is based on that supposed fact.
Then they suddenly start rushing like all hell broke loose. You can't even call it rushing anymore. It's like it's just listing bullet points on a powerpoint presentation without actually bothering to connect them or build up to them. Major events that would usually be (midseason) finales are happening one after the other. One episode they're dealing with Tinasha's main motivation for living, the next they're fighting a god, the next they're fighting demons of a different witch. In between all of this, Oscar's "curse" gets fixed as a sidenote. Oh, he also becomes the king somewhere.
One clear example of the rushing is episode nine. Oscar gets poisoned by a incurable ancient poison. Literal minutes later he gets cured by Tinasha, but she removes his memories of him (motivations for it are poorly explained). Barely two minutes later he remembers her again, finds her and sees she's now poisoned by the same poison and looks like she's dying. Next scene transition, she's totally fine and all is well now. All that took barely even half an episode. A lot more happens in that episode on top of that. That episode alone should've been three to five episodes.
Other times, the most important stuff all gets handled off screen and we only get to see the last bit and that's that.
The anime never recovers and then for the final episode they have the gall to basically retcon everything. All that happened no longer matters. Here's to season two.
Will they try to refer to stuff from season one in season two as if we're supposed to know about it even though they probably skippes it? Probably. Will it make sense? Probably not, as, again, all the important stuff was skipped.