First off....you could always try using yur fingers and ditching the pick. Many players hardly use a pick and get plenty of speed and a wonderful tone.
I would agree with every bit of advice given so far. I would emphasize a few.
1) Your pick. When I was first learning I thought the thinnest picks would help you play the fastest but after many years I don't think that's true. After moving on to harder and harder picks I now use V-picks exclusively. They have zero give and are like greased lightening for me. Plus, when you use a light pick you have to take a bigger bite with your pick to get a louder sound where as with a stiff pick you can have a lighter touch and get a louder volume. As per the handshake example Red mentioned .... lighter touch means faster release and picking speed.
2)If one hand is moving faster than the other you are not keeping time correctly. Use a metronome (there are very cheap electronic ones available) and practice with it. Set it for as fast as you can play, keeping both hands synched up. Keep it there for a week then move it up a bit. Do this each week for a month or two my guess is your left will keep up. Angelo speaks wisely, everything on the guitar needs to be perfected at a slower tempo before you move on....chord, leads, a new song etc. Play it slowly and correctly before you increase speed.
3) I have never found the way I hold the pick to be something I focused on. I use my thumb and forefinger with the point of the pick inline with my index finger. If you drew a straight line down the middle of the last joint of my index finger it would end at the pointy part of the pick. I probably leave 1/4" to 3/8" of pick exposed but again I have never really thought much about this and others can jump in with their technique.
Good luck and take your time. Think of what songs you want to learn to play and work up to their speeds. Unless your intending to shred or play speed metal there is no need to be superfast better to chose the right notes in a tuneful manner
Too soon we grow old, too late we grow wise
"I once played notes so fast that light emanated from the strings whereupon, I saw God.... who then told me to relax and start playing music."
"You know, once you've had that guitar up so loud on the stage, where you can lean back and volume will stop you from falling backward, that's a hard drug to kick." David Gilmour
Truefire Science Officer (dabgonit....where's my blue shirt!)