One Mile at a Time points to a Flyertalk thread with some (possibly momentary?) good news on the evil practice of United refusing to allow Mileage Plus members to book awards that are being offered by its partners (and frequently claiming falsely that the seats are not in fact being made available by the partner).
At the moment it seems that the blocking practice has let up some, at least for Lufthansa flights which normally seem to be the most heavily blocked flights for awards by United members. Reports are that intra-Europe flights are especially bookable, and some transatlantic flights too, including flights that Lufthansa had been offering but which United was previously blocking.
So now is a good time to try to book awards with United miles, or to make changes to awards already booked if a different set of flights would be more advantageous.