first off.. go to Windows > Settings/Preferences > Preferences
and find Polygons under Display on the left.
tick the checkbox 'border edges' and set the edge with to something like 4.0
this way you'll know the difference between an edge and a border edge. (i think it should just be on by default)
border edges are edges that are only on one face ( an edge is just a line and non-border edges have a face on either side of it)
now back to your problem...
it could be that the verts on a face are not quite seperated from each other so all you see is just an edge
in that case switch to face selection mode and (assuming you have 'whole face' selected in polygon selection under selection in the preferences window you have open) just marquee drag (click and drag so that selection rectangle is there) over the edge and then hit delete
if taht doesn't work then you've done something funny! so possibly try drag over a larger region of faces delete them and fill in the faces that you delete that you didn't want to delete with the append polygon tool
if that doesn't work then start again
that's a "Ch" pronounced as a "K"
Computer skills I should have:
Maya, XSI, Photoshop, AfterEffects, Motion, Illustrator, Flash, Swift3D