I'm looking for a more detailed dataset than the 1:2,000,000 shapefile available from the National Atlas, preferably one suitable for use at 1:24,000.
Since the continental divide is determined hydrographically, I would use data from the National Hydrography Dataset (NHD), or the analagous Watershed Boundary Dataset (WBD). Based on this geodatabase of HUC8 boundaries from WBD, the results look pretty good at 1:24,000 scale:
This shows Triple Divide Peak in Montana.
there's an ArcGIS feature layer that can be found here