What is the impact of one trailing edge rotary actuator failing?
The 747 has two motors per flap group.  The primary means of moving them is through a hydraulic motor, while the second motor is a backup electric motor which is only used if the primary doesn't work correctly.

There are also two groups of flaps on each wing, and they are mechanically linked to the same flap group on the other wing so that they always extend at the same time.

You are correct about a failure on the ground.  The pilots would take the airplane back for maintenance before they departed.  

In the unlikely event that both the primary and secondary motors failed, or if the flaps were to somehow become jammed and not extend once airborne, the flaps would not be able to do their job.  Since they wouldn't make the wing bigger or change it's shape to create more lift, the aircraft would be forced to land at a higher airspeed, which would cause it to use more runway.  This isn't a big deal if there is sufficient runway at their destination, but if not they would have to divert to a suitable airport.