If you haven't discovered so already for yourself, using a jazz pick seems to really help some people in playing fast and accurately, including myself. I used to use the black Dunlop nylon 1mm picks, which were pretty good, but I noticed I still got caught up on a string when alternate picking really fast.
But when I switched to a jazz pick (the one I'm using is a Dunlop Tortex 1.14mm), I almost never get caught up on a string. And there's a few reasons: it's slightly thicker than a 1mm pick, but more importantly, it's pointier and it seems to keep its point longer. Also, it's not nylon, it's made out of some material where no matter how sweaty your hand gets, it doesn't get slippery. My nylon picks even had bumps for grip and they were still more slippery.
The only thing I still use my nlyon picks for is if I'm playing all rhythm and strumming, because it's bigger than the jazz pick so it's easier to strum.
But if you like to play fast or shred, check out these Dunlop Tortex 1.14mm, they're awesome!
~Rusty