If you want to play something well, practice it slowly. In fact, the faster the piece, the slower the practice should be. Why is this?
For better or worse, we are creatures of habit. Whether it be your morning routine, where you sit at the family table, or which TV shows you make sure to watch, we operate best with a degree of consistency. This principle holds true with our musical efforts as well: how we practice is how we will likely perform. Therefore, playing correct notes, rhythms, dynamics, and articulations the first time and every time will more likely guarantee success in future performance. The best way to ensure accuracy in those first few practice sessions on a new piece is to slow it down — way down!
Only after you are comfortable and consistent with every aspect of musical performance should you allow the tempo to gradually increase, with an emphasis on gradually. Every increase in the metronome tempo (yes, you should be doing this with a metronome) gives you just a bit less time to think between notes and forces you to rely more on the habits you have created. For exceptionally fast passages, you will almost entirely be dependent, for better or for worse, on the musical choreography you’ve established through repeated practice, so slow, deliberate, consistently correct practice is critical.
Even if you’ve recently started a new piece, it is not too late to slow things down and establish accurate musical habits to ensure a better performance. Happy practicing, and when in doubt, go a little slower!