Sloppy guitar playing

You might want to try playing without any distortion at all. I've always found that when I play a riff with overdrive it sounds real tight, and then when I play the same part without it it's way harder to get it tight. It's as if the guitar and both hands feel less smooth (does anyone else have this experience???), and I have to work harder to get the stuff right. So this way of playing is a good way of getting your picking tight.
 
Due to the way I play ( I'm left handed, and I play with my strings strung right handed, on a left handed guitar ), and the size of hand, I have to anchor my pinky, otherwise moving my left hand would result in me nudging the strings and making them ring like a mother fucker, and my neck is not too large, so my hand towers over the neck.

Try what is best for you, though, don't just take others advice, cause it might not be the best for you, blah.
 
Look at your pick position, if i play fast i only have a minute amount of pick exposed maybe 2mm or less, never been good at measurements. Less pick = less getting caught and less friction. Basically slowly practice your picking, get the full motion from the wrist and slowly with a metronome work your way up. Also, muting wise, it helps to pivot your picking from the wrist as well i find, i also anchor my palm across the bridge (the pinky extended etc) moving it back and forth as muting dictates (onto the bridge and onto the strings and vice versa), be warned though, if you are playing on a floyd you need to avoid putting too much pressure on the bridge, or you'll go sharp.