Caveat: I'm not a super fast player. I
have spend a fair bit of time last year working on alternate picking technique, so I've definitely gotten some lessons learned, but I'm no pro. That said, it's the internet so I might as well give my 2c.

If you watch videos of a bunch of great alternate pickers - Petrucci, Malmsteen, Vai, Gilbert, Govan... they all have different styles. Some of those styles (like Vai's) look
really uncomfortable for me. There are certainly common themes - 1. stay relaxed 2. pick from the wrist, not the elbow and 3. don't anchor your hand on the bridge too heavily; but actual hand positioning is very much an individual thing. Everyone's body is different and what works for you may not be what works for your musical heroes.
In my opinion you have to start with the sound and clarity of each note and get the tone you want, then work backwards up your fingers, though your wrist, through your arms to get the whole process in sync to create that sound. If you're consistently flubbing notes, there's a reason. Slow it down and analyze. Is it pick angle? Are you moving your fingers to much? Are you flubbing because you're anchoring your hand on the bridge? I would always recommend playing slowly and accurately and building up speed from a solid foundation, but be aware that every technique has a certain speed at which it begins to
feel different. You need to push yourself and understand that feeling in order to play fast. If you only ever practice slow, it's hard to be good and fast. If you jump way ahead and just slop through playing fast, you'll never get clean. You may need to tweak your technique to make a smooth transition. Also, be sure to change things up and don't get stuck playing the same exercise over and over for too long. String skipping feels different from linear lines. Outside picking feels different than inside picking.
"It doesn't take talent to upgrade your playing. It takes patience" - Kenny Werner