Magical disappearing faces

So, I'm getting better at making and using 3D objects, but I've still got much to learn as it would seem.

After following the stickied tutorial for getting rid of black faces, I found that my object now has faces that disappear at certain angles of view. How might I fix this problem?

That's because getting rid of the black faces also gets rid of double-sided faces (this is assuming you're using sketchup). I don't know what settings to use to put double-sided face back, but that's certainly your problem. What I do is just make another face concurrent with the problem face in sketchup and reverse it. That tends to solve the problem. It's a bit tedious/awkward to work with, but it does work. Ask someone with more experience how to put double sided face back in sketchup 3ds models.