I had a rat's nest issue on an object created from an extruded spline. I was selecting points and welding, but in one spot, I had to delete the polygons just to be able to find all the points. I then used the Polygon Pen and Close Polygon Hole to replace the missing polygons. Now the texture looks as if it is applied to those polygons separately, as if they are not part of the overall object. I have tried aligning normals, reversing normals, changing point order, and deleting the polygons and redrawing, starting from a different point each time (which worked for me before in R15). Nothing works.
you had/have a texture that uses UVW mapping - taking out polys and then rebuilding doesn't put new polys in the old spot in the UVW structure. You can either remap to something other than UVW (if it will work with your object) or try to reset them yourself with Body Paint UV Edit - I don't know a lot myself but - using the UV Terrace command is pretty easy if the hole has polys surrounding it but things are a pain if the badly mapping new polys are object border polys.
Thanks for the reply, and sorry my reply is so late. I had to rush to finish that so I could start a new project (which is also giving me grief, of course). I wound up taking a backup copy of the extruded spline and welding or moving points around. I normally create a UV map for anything that has a texture - like wood grain, etc. - but that material didn't use a bitmap for the grain, so I thought it would be quick and easy.