The dead space is in reference to the amount of unused space at the top. So a typical 10g rubbermaid cooler is something like 10.7 gallons. If you ended up with grains and strike water at the 10g mark, you would have .7 gallons of dead space. The more deadspace, the less efficient the cooler is at retaining the heat as you will "lose" heat into the dead space.
If you calibrate your MLT in BTP it will take the temp loss into consideration. It seems to be pretty accurate as long as you follow the steps.
Edit: I'm not sure what kind of manifold you are using, but if you can get a slight bend just inside the spigot, you can collect almost all of the wort without tipping. I have about a cup left in the bottom of mine when I am done.