As others have shown, its certainly not impossible to do but, it will require a good deal of planning, maintenance and diligence on your part, as the water chemistry can go out of whack a lot more rapidly than a larger tank, especially if you live in warmer/drier climates or have air condtioning.
Probably the biggest concern would be evapouration during the summer months. Since its the virtually the only way the aquarium can cool down naturally, you'd ideally need to have an auto top-up connected to it, or run the risk of the SG level rising to dangerous levels by the days end. During the summer I was topping up 3-4 litres of RO water sometimes. That would be 1/3 - 2/5 of the water in your pico tank. You could put a lid on it to reduce the evapouration rate but, then you'd run the risk of the tank overheating.
Due to the smaller water volume, toxins from corals and other unwanted pollutants like nitrates and phosphates, rise to harmful levels quicker, all of which will be exacerbated by a high evapouration rate. Corals will also deplete nutrients like magnesium, calcium, iodine, etc, from the water sooner than in a larger volume of water too and so additives or frequent water changes will need to adhered to.
Although they can look really cute, they are certainly a lot more involved and harder to maintain than a nano tank. My advise would be to plan for eventualities like I mention above and think of ways to combat them. Increasing the water volume by connecting a sump is one possibility. A perstaltic dosing pump to feed an auto top-up system is also an option. Alternatively a chiller might be another solution. However, neither of the last two options are particularly cheap.
Hope that helps,
AK
*edit*
As far as livestock goes, you could probably get a shrimp in there, a few snails and maybe a micro hermit or mithrax crab until it outgrows. Personally I think its too small to consider any fish, even a goby. Aside from the space, the impact on the bioload from a fish would probably nuke the tank.
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