Using large coordinates is a nightmare in most of the 3d programs and SketchUp is no exception. Clipping issues, z-fighting issues guaranteed.
The only solution (that I know of) is to use a fixed translation (just write it down somewhere) for your project. Maybe your GIS app can do it for you already when exporting? Otherwise you have to do it in SketchUp yourself. Most of the time I just load the new parts in a separate SketchUp file, do the translation and then copy past it into the main file.
edit: typo

@markewi said:

The Measurement box isn't too handy...

You're right. At least if you don't learn how to use it. Read the Help article mitcorb linked to. If you want to move entities to a specific location relative to the origin, use [x,y,z]. If you want to move things to the ground plane, you can use [,,0]. What ever point you grab with the Move tool will be located at the ground plane.