I think for some reason the lines are not exactly touching the faces. You can fix it by selecting the lines, Cut, Paste in Place. You may have to redraw a line or two to heal it after that, but the faces will be good.
I have a lot of such elements in many modesl and it will take a lot of time to find and fix it manually. I tried to use Solid Inspector2 and RubyAPI to automate the cleanup process, but I need to intersect faces somehow first. Is there other way except manually remove and then add edges?
I did use your model, and it was Paste in Place I was saying to do. Paste is unlikely to put it back in the right place. Dave has a simpler work around.