Is the thin line usually woven in a contrasting color into the corner of a Navajo rug a flaw?

No. Through historical research and numerous interviews with Navajo weavers, Noel Bennet published "The Weaver's Pathway: A Clarification of the 'Spirit Trail.'" He concluded that to most weavers, the line allows a pathway so that the weaver's "spirit, mind, energies and design" are not trapped within a completed rug. However, some weavers frankly explain their mothers told them to add the line as some buyers expect to find it.