Distant earth-orbiting satellites can sometimes be mistaken from asteroids. Certain objects have perigees thousands of miles from the earth's surface and apogees even farther out. Again, these are extremely challenging objects to find and observe. Assisting in the investigation of such mystery objects can help to determine the truth about their source orbits. Observing transits of satellites across the moon or sun are another challenge for satellite observers.
Space debris includes a wide range of objects size-wise.
The smallest debris, such as results of explosions, can also present a major challenge to observers. They can give clues as to the reflectivity of objects in comparison to their radar cross section. Imaging the shape of a satellite using a large telescope and auto tracking is a mostly unexplored field that offers lots of new horizons. The International Space Station offers a sizable target whose shape can often be discerned in moderate sized telescopes. Observing and monitoring light curves of moving satellites offers a good training ground for persons wanting to learn magnitudes and develop acuity skills that can be applied elsewhere in astronomy such as to variable star measurements.