Not totally sure how to get what you want, but what you did in that particular place is extrude once, then you didn't move the new vertices at all and extruded again.  If you look closely in edit mode (face select only, like you have in the image) you'll see 4 little squares on each of those edges.  These squares represent the middle of a face.  You've got 4 extra faces in there with no area.  if you select everything and then remove doubles ("w"-->"remove doubles") those squares will go away and you will probably lose that line in object mode.

You do get more than just the outline in object mode, you get all lines where the angle changes by some amount.  All the lines you have there except for the outer lines are between flat faces with no change in angle, so you won't get a line there.  Not really sure how to change it to show all lines, but I'm sure someone around here does if it can be done.