Try to avoid drop shadows, especially ones with large shadow diffusions. Creating text or images with drop shadows that will be floating over a colored webpage background are another special case altogether. That's because the image was made on a white background, then the background was made transparent, and finally placed on a colored page. If you've got shadows you intend to float over a color, make the image with the target color in the background. You can then make the background transparent as you produce the gif, and the shadow will look more natural.
Gradations are a big no-no on the web, particularly subtle ones.
Avoid them if at all possible. Use GIFs for flat color images and line art. This palette contains the web safe 216 colors which work on both PC's and Mac's. Very important, and useful for avoiding headaches later. Another good palette resource is here .