[timcharlto]

If I boil a substantial amount of water away would the remaining liquid be noticeably enriched in 18O?

[OC pro]

It is not that simple. But in principle yes. 18O-enriched water is obtained by distillation.

[Enthalpy]

http://en.wikipedia.org/wiki/Isotopes_of_oxygen
tells the effect of the more selective low-temperature evaporation: atmosphere 0.204%, fresh water and polar ice 0.1981%, seawater 0.1995% - it would take at best 22 cycles to gain 0.1% concentration, how bad.

http://www.isotope-cmr.com/index.php?page=oxygen distillation of water: 100,15°C versus 100°C
http://www.iconisotopes.com/Code/Oxygen18.asp distillation of nitric oxide
http://www.marshall-isotopes.com/p.htm distillation of water

I thought they would use centrifuges, diffusion...

Are you looking for a clean neutron multiplier to produce tritium at ITER? Wish you to succeed then, because lead spallation would make D-T fusion as dirty as uranium fission.