The 10m and 50m raster data on the NE download pages are updated and now contain corrected TFW files. The 1.0.0 files were a tiny bit off in their extents, the new 1.0.1 files are now perfectly within the ±180, ±90 bounding box.
The bad extent was throwing an error for some GIS systems on import and leaving gaps when reprojecting in the area of the international date line for others.
We’ve tested in ArcGIS 9.3.x in NSD Pro 5 georeferencing the rasters with the TFW files and reprojecting them. No funny gaps appeared at the 180th meridian. Thanks for edcorkery and user4815162342 in the Forums for first discovering this and Hans for the solution. Please let us know if you still experience reprojection problems.