Use the Cleanup plugin to get rid of those extra faces you have piling up on each other. What is happening is that often when you delete a line and redraw it, or if you draw two lines on top of each other, SU will make two faces on top of each other (even though everything "looks" normal). You have to go through and delete these extra faces or just run Cleanup plugin to get rid of them.
But, that aside...
You have to think of 3D print modelling just like you would be building something in real life. Every wall has to have a thickness: in other words, a FACE is NOT a wall. A wall must have two sides and a middle (thickness). 3D printing does not know what to do when you just have a single face because it sees this as a piece of geometry without any solidity.