I inserted a circle and blurred it. Now I can't remove the blur, and subsequent shapes I insert are also blurred, including the square and star shapes. The blur is off in the "Fill and Stroke" section and I've gone through every option in the drop down menus.
Check the Objects panel. There you can see blur and opacity settings for individual objects, groups and layers:
If you have blurred a layer or group every new item in that layer or group gets blurred.
Select a group or layer in the objects panel and remove its blur. It doesn't make individually blurred objects sharp, you must adjust them separately.
BTW individual objects should be blurred in the Fill&Stroke panel because there you get better adjustment accuracy.