I am having trouble getting things to line up correctly with the object manipulation tools (specifically rotation) because they are so sensitive I can't get the finer movements in. Is there a way to turn down the sensitivity, or possibly another way to more finely rotate objects?

This can be done in "Preferences" under the Movement tab. Speed, angle, and grid size will probably set you straight. Alternatively you can do it on the 3D Data tab of the Reference Editor. I don't consistently do one over the other.