There's also a way to skip just about all of level 13... if you do it right. People always seem to complain about how you don't have enough time to get through that giant electric field, but I've never set foot anywhere between the field. If you aim just right on the wall, you can step out onto the empty space in front of the wall portal and shoot a portal on the floor in front of the entrance. BWAHAHAHAHAHA!
I think I know why the invisi-wall was made. If you look at the screenshots, you clearly see a backwards portal to his left. Maybe it's the strangeness of the fact that he's behind a portal that caused the glitch. Also, first post here!