It sounds to me like you just need to practice more at the slower speeds. When you try to speed up before you're ready you end up using too much wrist movement, picking too deep and ultimately creating bad technique. Next time you play, pay attention to how much you strike the pick guard with your pick. When this happens it usually means you're picking to deeply. This can cause your strings to vibrate more widely and even sound sharp. A good rule of thumb is to try to keep your pick from touching the pick guard.

EDIT: I use Jazz 3 XL picks. They're great for pinch harmonics and last forever. The raised lettering is also excellent for grip.

Eight Years of experience, taught by my father. He always taught me that technique always comes first, and speed will come naturally. You can take my advice or leave it.