Apparently I already noticed this problem (see #287) but thought it was restricted to ArcGIS 9.3. Turns out it occurs on 9.2 as well (and probably 9.1 but I haven't checked).
This is a major problem. There are hundreds of these for the "crude" resolution GSHHS database and thousands for the higher resolution databases. These are mostly lakes that are too small or oddly shaped to be resolved by ArcGIS.
I spent a lot of time playing with environment settings such as XYTolerance, XYResolution, and so on. No matter what, when I wrote these polygons using the geoprocessor's InsertCursor, they would be stored with null geometry. I verified this by reading the feature class with OGR; it reported that there was no geometry for these polygons.
I also tried writing these polygons with OGR. This was successful. ArcCatalog and ArcMap could even display them. But when I ran Check Geometry on the feature class, it reported "self intersection". When I ran Repair Geometry, it reported "self intersection", corrected on each polygon, corrected it, then reported "null geometry", and then deleted it.
Try as I might, I could not get ArcGIS to recognize these polygon slivers. I will update the GSHHS tool to run Repair Geometry immediately after writing the feature class to remove these, and issue a report about which polygons it removed.
Thanks to Barry Eakins for reporting this problem.