Dr Geep!  Fancy meeting you in a place like this.  I thought you only were hanging out in the Poser realm for some reason. lol.

Thanks for the suggestion Dr. and thanks for the tutorial there GKDantas!

I have now solved my problem thanks to your help.  I had simplified my problem a bit when I posted here, but let me elaborate.  I actually had two neighbouring polygons that were misbehaving the one highlighted above and the one directly below.

I had tried the fill polygon first, but since the area that was being worked on was pretty complex (I'm guessing)  it wouldn't fill.

So I drew in the ploygons by using the polyline tool and then filling it on close (I missed the polygon tool entirely!)

The result was two polygons that then refused to weld into place.

After viewing the tut, I decided to go and delete the two polys I had made and use the polygon tool instead.  I also chnged the area to three polygons sue tot he way the one was being forced to warp.

Anyway, after doing it that way, I found when I moved the area that there were two lone vertices hanging out, not attached to anything and just hiden behind the mesh's vertex points.  I think these guys were what was causing some of my problems.  They must have been remenants from when I was using the add tool to create new lines int he mesh.

Anyway, all is good now!  Thanks for the help!

Cheers!