.....a passage can be played flawlessly at a reasonable [slower] tempo, then the time comes to see if that passage at tempo works with the initial fingerings and gestures practiced at a slow tempo. It may or it may not. So. you make the necessary mid-course corrections.
When we practice at slower tempos we must know when to play physical movements that correspond to normal tempo mode. This is to say that correct slow tempo practice is a combination of slow movements but also the faster movements which correspond to normal tempo.
We must always ensure than our actions emulate the normal tempo, so if you are playing something with a lot of arpeggios slowly, you must make sure than when you move to a new group of notes, that the movement is as if you where playing at a normal tempo. The same applies for chord changing, we must change the chords as fast as possible, as if we where playing it at normal tempo, there is no slow lifting and slowly placing fingering onto the notes, then playing them. You must pause as long as you like, then when you know where to move, move there immediately. This might require a fast movement of the hand which seems strange to do if you where playing at a slower even tempo. So you must know when to break the slow tempo motions and make movements which correspond to the normal tempo.
I guess this is a misconception, that slow practice requires slow even tempo in our hands. In musical tempo it will be even, but in our hands we are constantly switching between a slow easy motion and the faster motion of the normal tempo. Perhaps when you are learning notes you can play as slow as you like any way you like, however when you are targeting the technique to control those notes your movements must not follow an even slow tempo, you may only have this slow even movement when your hand does not have to move position. If your hand is constantly moving then you can learn how to break up this movement into its points and know where you can pause between the movement and not destroy the appreciation of the overall muscular memory. There are certainly situations where we cannot properly appreciate the muscular memory association if we play slowly, the opening RH jumps of Liszts La Campanella is one random example.
I'm no teacher... but I think you need to find out how you learn best (to paraphrase bernhard)
I have found through experience that not many students know exactly how they learn best in every single aspect of keyboard study (and it is something that is a challenge for a teacher to diagnose in their individual students and this requires a lot of questioning from both teacher and student constantly.). "Knowing what is best for yourself" is certainly an ability good teachers will instill into their students in many areas, but to ask a student to do so in ALL areas required from the study of music requires an advanced knowledge and a lot of experience. Even if you are autodidact you still need to rebound your ideas off an experienced teacher to test and refine your method.
Memorising music is such a large discipline that to be completely confident that you know all the ins and outs of the process is quite presumptuous. I am always learning something about memory from other people of all abilities of the piano. The way in which people deal with memory is an interesting observation for the teacher. We suggest to the student OUR catalyst towards memorisation, observe how that effects the student and then alter the catalyst so it suits the student.
It is asking a lot of an early beginner or even an intermediate student to understand how to learn their music in the most efficient/effective way. Even advanced students need to have their practice methods scrutinized but of course not as much. We never stop improving our way on learning music just as we never stop improving our ability to play our music. Some cannot constantly monitor their methods, they reach a plateau in improvements they can make, thus having a teacher or someone who has more experience than yourself is helpful to further make progress.
Nothing can be done perfectly, we can never achieve perfection but we can aspire towards it and know when we tend away from it. Everyone can sense when they are tending away or towards improvement but at which rate do you tend towards it? I find some people the curve towards perfection is too gradual, so as a teacher we can bend this curve so it moves faster towards perfection.
Topic: Speed Learning