Why does Google Maps Display Routes/Waypoints Differently on Phone than on PC?
To answer the original question, according to Google's official post, Maps on the phone take real time traffic conditions into account when calculating directions.  This could explain the discrepancies between the directions you found via PC earlier.

The bug you are describing could be a side-effect of this, when Navigation is trying to be too smart for its own good, and the route from web is confusing the computation of real-time directions.  I would submit this as a bug report to Google.