Shadow Priests vs Melee right now are fine if you play properly.
If you're being snared or rooted or whatever, then it's time to play defensively. Throw up heals, use your shield, etc.
Also keep in mind that Interrupts and Silences are two totally different things. If one school is locked out, then it's time to start using the other school. Usually healing yourself when locked out of a shadow school is the best thing you can do.
And then you have your 4P mooncloth, your fade, and your disperse.
And if you happen to be worgen, you can disperse and dark flight to a safe distance.
It's all about how you play. I know that Shadow Priests, while on the move, can't do much in the way of nukes, but that's just how it goes. I'd much rather have Mind Spike be castable while moving to be perfectly honest... that would give us a reason to use the paralysis talent and it would give us a nice nuke that we could use while on the move.
---------- Post added 2011-04-23 at 05:50 PM ----------
An idea would be making it so when you proc Arch Angel, you could also cast your spells while on the move.