There are some technical details in making this work that you have to explore. If you want to study solar system objects, you can always monitor surface features on Jupiter and Mars. This will depend on just how good your telescope is and the quality of your local atmospheric seeing. Try your hand at searching for comets. You can study the changes in the appearance of already discovered comets such as the new and exciting 'Hale-Bopp' comet due to arrive in 1998.
Photographic studies are best.
The rotation axis of the Earth does one complete cycle every 25,725 years. In 100 years, the location of the north celestial pole moves 5500 seconds of arc relative to the stars. A several hour time exposure would show the stars trailed into arcs, whose geometric center is the North Celestial Pole. You would now have to have some landmark on the Earth that you could see in the star trail photographs and against which you would measure the pole shift. This is the best I could do in 15 minutes.