Distilled water is slightly different in its properties for freezing, boiling, etc. as it has no dissolved elements. It takes a lower temperature to freeze water with salt, and a higher temperature when some salt in water is brought to a boil. Water is still heaviest at 4 deg C, but salt or other dissolved substances in water seemed to have some effect. Distilled water is probably a more aggressive solvent as it has nothing in it, so it is hungry water, wanting to grab sediment, nutrients, elements it comes in contact with.

Thank you, Hansen.

Water properties resulting from cycles of distillation be still same as distilled water? That is, do we have any fatigue properties in pure water, which it may loose due to repeated stresses? Pure water is just water molecules (without any dissolved solvents or minerals).

I am more interested in the fundamental properties of water, which would help in understanding Quantum Coherence property (Quantum Electrodynamic theory), water thread experiment or water floating bridge experiment and Emoto's water experiments (affects human consciousness has on the molecular structure of water)-

http://www.i-sis.org.uk/Quantum_Coherent_Water_Life.php

I guess a distillation of water will involve change in isotope composition, thus a distillate will be enriched by regular water as compared with a reminder enriched by heavy water which has essentially higher boiling point (by more than one grad). H2O, D2O, HOD have all essentially different properties, may form different hydrogen bonds, and have different diffusivity. They will differ also in an ability to dissolve chemical compounds. Differences are not necessarily drastic, but they are not negligible However, in vast majorities of the processes, distillation will result in a very limited enrichment extent,, and, therefore, in a negligible impact on physico-chemical properties of bulk water, until the distillation was not multiply repeated. 

Dr. Mikhail, thank you for your comments.

Water is never pure for there is not such thing as water without any impurity. At a given point of time there are some hydrogen ions which immediately transform to form the water molecule similarly the molecule itself is never stable these bonds keep breaking. The best example is a comparison of stored water and fresh water, only the human taste can make out the difference but there is no way that it can be differentiated by a test. The water molecule is pure as itself but the contamination factors can make a change to the water, simple boiling of the water can change the very taste of it for water is in a constant state of transformation, apparently following the arrow of time.