Welcome to the cold waters of 5.4 shadow!
Here's just a few tips off the top of my hat:
1. Practice maximizing dot uptime before anything else, it's the backbone of your dps (especially when you can multi-dot). The optimal way to refresh dots is usually NOT to refresh them at the same time (there's 2 exceptions though, strong int procs, or if both dots have less than ~5s duration remaining and you are about to do a 3 orb plague with Insanity talented). VT and SWP have different durations and VT expires before SWP after the first application.
You'll want to refresh each dot manually -just- inbetween the last two ticks of the dot (~1s mark), to gain the maximum amount of ticks for each dot possible. It can be a hassle at first, but you'll gain many dot ticks over a fight that would have otherwise been wasted on an early refresh.
2. It's very handy to have an addon like WeakAuras configured to show you clearly when strong procs are up, like trinkets or legendary meta. This is important as dot snapshotting is for now still a thing and refreshing them during strong procs yields a massive dps gain.
3. The addon HaloPro helps you maximize Halo damage, I consider it almost mandatory for any shadow priest, as the Blizzard standard UI simply lacks any clue to show the optimal range to launch Halo from.