The hypothetical swimming pool is inside a habitat at atmospheric pressure, and on Mars at 0.38g of Earth. What are the major differences regarding water properties (viscosity, surface tension, cohesion, does it feel like gel...) and how would the swimming astronaut compare the experience to Earth.
Shortly after this question was asked, it was answered (in the case of the moon, not Mars) on XKCD's what-if.
Summarizing that article, for most average people swimming would be the same, as the buoyancy effects are an order of magnitude more dominant than the gravitational effects. Extraordinarily skilled swimmers would notice small difference, but the real differences would be in activities that break the surface. For instance, humans could leap out of the water like dolphins. Jumping out of the pool would be an actual jump. And with a monofin, you could high dive onto the diving board:
Its much harder to swim fast, even though it might be easier to swim slowly.
Your main difference will be due to a reduced hull speed of the swimmer. As noted in the comments section, the phase velocity of a wave would be reduced. This forms a hard limit on the speed that one can swim whilst displacing water.
As you swim, you generate a wave. If you swim at the speed of the wave, you will be swimming in the trough of the wave, which is basically flat. As you try to speed up, you find that you will need to swim "up hill" against the wave. This is what we call "aqua-planing" or as we boaters like to call it "planing".
At this point the equations of motion become much more complicated, but suffice to say drag increases significantly.
See http://en.wikipedia.org/wiki/Hull_speed for more information (note, the calculations there assume 9.81m/s^2 local gravity).
There's one consideration probably neglected by most answers: with water viscosity unchanged, it will be much easier to remain on/above the surface through actively "pushing against the water" - unlike on Earth, where it takes a lot of (futile) effort to remain immersed any less than what your buoyancy gives you, a couple strokes will get you sliding along the surface of water.
With strokes like front crawl you'll be easily able to bring yourself to the surface, and then only immerse your hands for propulsion, while your body skims the surface, barely creating any wake wave. Of course if you want to remain immersed or dive, it just requires you to angle your hands differently and "pull yourself under", but if you want to move fast, you can move like a speed boat, barely skimming the surface.
I guess with gravity low enough and the right technique, even running on water could be possible - not due to buoyancy but because so little force is needed to stay airborne.
Wave height will be bigger, right? And of course, droplets and splashes will take longer to fall. As your head leaves the water, surface tension will try to hold water blobs onto your face, which could also interfere with breathing. You might need to adapt your swimming style somewhat to avoid these effects, like shaking your head in a side to side motion and timing your air intake differently.