This is a really super fun question. I only wish that Randall Munroe, not me, were answering, so he could draw cool pictures.
Basically, what you are asking is what would happen if all the water in the ocean were suddenly turned to heavy water, deuterium oxide. Well, let's begin then...
Deuterium oxide has properties that are quite different from light water, the normal water we deal with every day. In general, it will be more dense, have a higher freezing point and boiling point, higher viscosity, higher activity, and most importantly, a higher heat of vaporization and heat of fusion. I've copied this chart from wikipedia to illustrate the differences:
If the change happened suddenly, then there would be all sorts of problems:
- Every ship, swimming bird and floating coconut would suddenly be displacing a lot more mass than it was before. In the absence of excess ballast, every ship would rise until about 9.6% less volume was displaced. Going forward all ships would either have to carry a lot more ballast to operate as designed or displace much less water.
- Water skimmers and other things that rely on surface tension of the sea might start having a harder time.
- A large portion of the oceans would instantly freeze due to a higher freezing point. This would release a lot of heat into the atmosphere in the polar regions, causing a massive imbalance and resulting in some pretty spectacular polar cyclones.
- Every single floating ice cap (newly augmented by the instant freezing event) would suddenly have enormous buoyant forces placed on it due to greater mass displacement. The effects are most pronounced in Antarctica. Some ice sheets break apart in an epic release of potential energy and others "bounce" immediately, causing tidal waves from the distortions. This is starting to sound like a Michael Bay movie.
- All waves in the world suddenly become less exciting, as viscosity increases. Of course, this is before the tidal waves arrive.
- All living creatures in the sea suddenly have a severe physiological imbalance. On top of the sudden change in pressure which has probably already discombobulated them, they begin to expose their cellular processes to heavy water immediately. Most will feel a slight tingling sensation, followed by death.
- Immediately, the equilibrium level of water vapor in the air begins to decrease, on average. The world becomes a place less prone to precipitation, as the amount of energy input remains constant but the heat of vaporization of most of the water on Earth increases.
- Replacing the volume of all the world's oceans' worth of water with deuterium oxide also affects the mass of the planet and gravity. According to the NOAA, (How much water is in the ocean?) there are 1.335E9 km^3 of water in the oceans, about 1.335e21 kg; changing all of that to deuterium oxide will add 1.48e20 kg of mass to the Earth. Since the Earth's mass is 5.97219e24 kg, the total mass of the Earth increases by 0.0025%; gravity will be correspondingly higher by just that amount. This wouldn't change much for us here, but almost immediately GPS would stop working, most geostationary satellites would need to be adjusted and many other space objects would begin to de-orbit. The moon's orbit would change, with its periapsis and apoapsis coming closer (thanks, Kerbal Space Program!) and the period of its orbit decreasing slightly, but fortunately, the Earth's additional mass would exactly cancel out the additional gravitational forces between the Earth and Sun. Less than fortunately, your question doesn't specify the angular momentum and linear momentum of the additional mass, so I can't comment on how the Earth's rotation might change, except to note that it will probably cause more tidal waves.
- A more catastrophic change is the volume expansion from the change in mass relative to the change in density. Since deuterium oxide has a mass of 20 Daltons and light water has a mass of 18 Daltons, the mass of water in the seas increases by about 11.1%. However, density has increased by only 10.6%! So the total volume of the oceans suddenly rises by 0.45%. This doesn't seem like a lot, but it would be even more like a Michael Bay movie. This would be the mother of all eustatic sea level rises. I tried desperately searching around for someone's records of the volume expansion that corresponds to sea level rises, but failed. Instead I guesstimated it by calculating based on the current surface area of the oceans. If you expanded all the volume of the ocean by 0.45%, assuming a surface area of 3.6e8 km^2, it would result in a massive 54.75 feet of water above the current surface of the sea . That's 16.69 meters. That's on top of the volume displaced by new ice formed from suddenly crystallizing heavy water - since it hasn't come to an equilibrium yet, it will still produce a rise in overall sea level. Expect some awful floods and a lot less land area. It'll be like that movie Deep Impact, except without Elijah Wood's sad eyes facing the oncoming waves - and let's face it, Barack Obama is no Morgan Freeman.
- This also all results in changes in pressure on tectonic plates. It may not happen immediately, but between the floods and the earthquakes I doubt California will survive.
- The tides have lower magnitude due to the higher density of the sea involved... but you won't care, because you and everyone you love will be underwater... unless you live in Denver, in which case I'm jealous for reasons that don't have to do with the coming heavy water apocalypse.
As for the long-term consequences... the important thing to understand about water is that it is connected to all living processes and to the overall water cycle. Any change to the ocean is going to percolate through all living organisms rather quickly through biochemical processes and that water cycle. And not just as water - the hydrogens in water, and thus the deuterium atoms in this case - ultimately will be inputs into our bodies.
Eventually, deuterated water will show up in our water supply, first in desalinated water, next in surface water resources from precipitation, and finally in groundwater. Within the first day or so we'd notice the differences. Deuterium water tastes worse, probably slightly bitter, and will be heavier than expected. In addition to bloat (because of volume expansion) and a perceptible increase in weight, in the long term deuterium oxide is toxic. Initially the short-term consequences will probably be minimal; deuterium oxide toxicity isn't really an issue until 25% of our body's water is replaced with it; there is some lower blood pressure, but nothing too serious. From animal evidence, however, we know that 25% bodily content of deuterated water makes us irreversibly sterile. Once it gets to above half, the buffers in our physiological systems get wrecked. It's fatal.
Plants will probably do better initially, but the lower surface tension in heavy water and the higher density means that trees will die above a certain height as the maximum height that water can be brought to by surface tension comes way down. Because heavy water makes eukaryotic cell division impossible due to its impact on the mitotic spindle, plant seeds will not germinate when only fed heavy water. Plants will live, but be unable to grow or regenerate lost cells initially; after about 50% heavy water concentration is reached, chloroplasts are unable to photosynthesize.
In addition, because water spontaneously ionizes and reforms, any light water that mixes with deuterium oxide will almost instantly become a partially deuterated water. When the rains fall, they soon drop larger (due to lower surface tension) and heavier raindrops filled with thoroughly deuterated water. Within a year or so, most bodies of water will have adapted to the new equilibrium. Plants would be unable to photosynthesize and all eukaryotes would be unable to undergo cellular division. Nearly all eukaryotic organisms will go extinct within a few years.
Since most heavy industry operates relatively closed cycle with respect to water, process industry won't start failing until significant precipitation changes the properties of the makeup water. Coolant loops would be affected first, while boilers might be alright for a while. Industries that need to continue functioning would need to implement light water filtration systems while the rest of the world frantically redesigned all steam systems to use the new properties of water. One notable exception would be the heavy water nuclear reactors, whose procurement problems would be over.
The very water turned to poison, the earthquakes, tidal waves, rising sea levels and social upheaval taking most of their brethren, the last humans will survive drinking bottled water, pumping the last light water from deep aquifers, Lake Vladivostok, and the Evian bottling factory, or desperately running hydroponics facilities with carefully hoarded viable seeds next to heavy water working fluid, nuclear-powered light water refining centers, ever conscious of THE END.