Simple Distillation of Unknowns
Ok, back to the start on all of this....

If you were looking for pure compounds or azeotropes what I'd want is a setup where a fractional distillation column was used with a very precise thermometer and a balance measuring the weight of the distillate. You could then nicely plot temperature vs weight. 

Assuming that you just want to detect the pure compounds and/or azeotropes and not collect them. 

Part of the problem here is that it takes some time to get the whole fractional distillation column up to temperature. So the temperature of the first drops is suspect. 

If you're using a heating mantle you might be willing to boil the pot dry. But you wouldn't want to do that with a flame. So you might lose a bit on the back end of the distillation too. 

The fractional distillation column doesn't have an infinite number of plates so the transitions from one compound/azeotrope to the next will be a bit "fuzzy." So if you were trying to collect "pure" compound/azeotrope fractions you'd avoid collecting the distillate from the transitions in those "pure" compound/azeotrope fractions. 

Does this help?

EDIT

I guess I'd like two thermometers. One over the pot and one at top of the fractional distillation column. 

Some sort of computer controlled temperature setting for the pot would be nice too.