Actually, a LOT can go wrong repairing iPads...much more so than with iPhones. The reason is that the LCD and digitizer are fully exposed and often times the battery is not properly disconnected/isolated prior to disconnecting the LCD which can create additional risks.
I see three separate issues in your situation:
# The first is the intermittent touch of the digitizer after repair. This could be caused by a poor connection but you validated that as a non-issue. Realistically, it could be a tear in the flex or just a bad digitizer.
# The screen jumping leads me to believe that the LCD may have been damaged. It is extremely sensitive to damage. Just torquing it the wrong way during disassembly or applying pressure along the edges can damage the delicate traces under the tape.
# Now the device appears unresponsive.
Is the iPad recognized when you connect the iPad to an iTunes enabled computer? If it is, at least the logic board is booting up and you problem is probably display related. When you connect it, also shine a bright light on the LCD. If you can see a dim image, the the LCD portion works but the backlight doesn't.