Look closely at the digitizer cable before you reinstall the screen. The cable is wider at its base and that part sits flush against the panel when you receive it. It doesn't look like it goes quite alongside the display data cable, but it does; do a quick check to make sure that both are the same length, and if they're not, look to see if the wider part of the cable is not pressed flat. You'll need every millimetre of length to connect it properly.
Also, you might be tempted to believe that the digitizer cable goes through the small hole above where the display data cable goes (it's pretty hard to see where things came from when you first remove the display). It doesn't; it nestles right against the display data cable. If you try to put it through the small hole, you're apt to rip the top off it by accident. There's really nothing more frustrating than painstakingly taking apart an iPhone only to break your replacement part.