Where does the thrust come from to keep it rotating despite the loss of energy from dipping into the atmosphere and grabbing a payload? Such thrust can not be applied on the spacecraft itself because the angular momentum would be insufficient. Rather, it would need to be located far along the tether without entering the atmosphere.

The movie was grossly out of scale. The spacecraft would be only a few meters (or tens of meters) in length, while the tether would have a lenght of thousands of kilometers. Controlling such a huge and massive structure would be a formidable challenge.

The only possible materials from which it could be made would be carbon tubules or aluminum oxide fiber. These can be made with tensile strength per unit weight some 100 times that of steel wire. In addition, aluminum oxide is highly resistant to extreme heat and totally immune from reaction with atmospheric oxygen.

Still, such a structure would be very hard to stabilize. To make it sufficiently stiff and strong, the tether might well have a mass of hundreds of thousands or even millions of tonnes. I just don't believe it will turn out to be feasibile.