Precise and smooth finger motions are the key to technique. This is true for slow notes as well as fast ones. Fast notes are just coordinated finger motions, the fingers don't need to move any faster. And it's possible to practice just the motions. I was impressed watching one of my son's piano lessons the other day, how his teacher wanted just a particular smooth circular movement from the wrist and arm. When done correctly, the notes underneath came out in a beautiful flowing torrent.
I've long been convinced that my fine motor control is worse than average. Among other things, I get a shaking tremor in my fingers, sometimes vibrating more than a cm back and forth. I know a bit about it: it gets worse under fatigue, or anxiety. It runs in my family, so it's likely genetic. I'm mostly convinced it's some mild variant of Charcot-Marie-Tooth, though I've never been diagnosed, and not that knowing the name would help anything. As far as playing goes, it's evidently not so debilitating that I'm unable to play at all. However, I constantly have to put a great deal of attention into my fingers, and am always wondering how "normal" my experiences are. Not that that matters either. We all have flaws and advantages, and have to compensate for them and use them as best we can.
Looking for information, I found this video on focal dystonia. Dystonia is different, since it's acquired, not inborn, and likely acquired through overtraining. It's sometimes career ending for musicians, though. Certainly watching that saxophonist attempt to work the keys kinda squicked me out. Although the causes are different, I wonder if the exercises that get suggested for dystonia would be helpful me.