Crystallisation and crystal surface It is my understanding that if you put table salt (as an example of polar compound) in water, the Na+ and Cl- ions will freely move through the solution. They will make the solution conductive and will independently travel through it to carry electric current.

Now the thing is, if you dry the solution, how come every Na+ finds it's Cl- to recombine into NaCl? How come there are no lonely Na+ and Cl- pairs who couldn't find their mate in time, before the solution dried completely? Can someone give me a better understanding of how do polar solutions work?
The crystal structure of NaCl forms at the growing surface of the crystals, where there is plenty of time for the ions to sort themselves into a regular lattice. Further, each ionic species is very evenly distributed also in the solution, because of the repellent electrostatic forces between the members of each. Whenever there is a local excess of positive or negative charges, it will level itself out very quickly.

If you have something larger than sodium and chloride ions and try to crystallise very fast, you will indeed get an increasing amount of errors in the structure. Freeze-drying also tends to leave behind rather unordered structures. In both cases, this is, of course, more likely with noncharged or even nonpolar substances.