Problem: A shape containing a pole does not reproject correctly
The original data is in the Two-point Equidistant projection. An ocean polygon completely contains the north pole and crosses the +/-180 line several times. When it is unprojected (or reprojected to Robinson), it becomes an inverted polygon.
This is a known issue. The projection horizon and clip/close code do not figure out that the pole is with the polygon. When unprojected, the polygon should extend from -180 to +180 in longitude and up to +90 in latitude. Instead the polygon is connected directly from the two endpoints at +/-180. The resulting shape is no longer a polygon. Depending on the rest of the data, a fatal ArcMap error can occur when ArcMap cannot reconcile the data properly.
Solution or Workaround
This issue has been resolved at ArcGIS 8.1.2.