Does Dean Kamen's Slingshot really filter virtually everything?
All it does is distill water while keeping heat within the system.  There isn't much detail provided about it but heres what I can say. 


  I have a hard time to believe this as: -chemicals could evaporate before water and so get into the distilled water -I have no idea how he keeps the distillation chamber clean (prefiltering?) so it does not clog.


While you are right that chemicals can evaporate with the water this is not usually of concern if the water source is not severly contaminated with volatile chemicals (as opposed to biological and soluble toxins).  If you were to have chemical contamination you could use reverse osmosis or activated charcoal to remove residual contamination.  typically this is not an issue though.


  I know that distilled water cant be drunk as it is without adding salts. I like the project of Mr. Kamen very much, I just want to know the boundaries, as the promises ("Fill in anything that is wet") seem way to optimistic.


Distilled water can be drank.  It may not be the most tasteful water but it does taste better than cholera.  If you want more information his TEDMED Talk is very informative.