Well after doing some extensive research and reading (googling it and reading Yahoo forums) I can surmise that yes, it is possible to extract DNA from faeces but it is not the best and most reliable way to test for DNA.
Firstly poop in itself does not contain pure forms of DNA. Poo contains all kinds of stuff: dead red blood cells, corn, multiple bacteria, lego and some DNA in the form of white blood cells that are usually deposited on the outsides of the turd as it passes through the walls of the colon, and epithelial tissues from the mucus membrane in the rectum.
So technically, there is potentially DNA present on poo. But if you perhaps were to mash the turd accidentally, then surely the DNA on the outside of said turd would likely weaken when mixed with the less DNA-rich inner turd, making it less reliable for testing? Aaaaand lets think about this logically, if you were smuggling a turd out of the toilet (somehow before it was flushed away) then it would have been sitting in toilet water for a while, right? So then wouldn't the DNA globdules have kind of been washed off the outside of the turd? Or even tainted with the remnants of other turd DNA? Yes this is likely. That is why is suggested that you do not let said turd hit the water. You have to catch that blighter mid air. Or catch it in a container before it goes ka-splash. See, highly impractical.
Some believe that due to the nature of the journey through the bowel, the DNA testable cells are actually deposited throughout the stool, making the whole turd (even a mashed one) suitable for testing. So though poop can technically be used to test for DNA, it's kind of a gross option unless you really need to specifically test your poop for health reasons. Researchers have found testing poop for changes in DNA is an effective way for screening for colon cancer. All you have to do is order one of these DIY poop kits and send your shit away to be tested! Eeew.
But the truth is, if you really want to go to the hassle of testing something for DNA then you are better off going with a hair with follicle attached, a cheek swab (though this is harder to do in stealth mode) or finally my personal favourite for stalkers - toe or finger nail clippings! Yum. All of these things are a much more reliable way of testing for DNA. Though of course, bone, blood and skin are by far the best biological specimens for testing! - Though these are more popular forms for crime scenes, not live people.
In my extensive research I did happen upon this interesting website that uses DNA poop testing to identify the dirty bastards who let their dogs crap on your lawn (or worse, on the footpath outside school! What's worse than scraping dog shit off your shoe? Scraping shit off the buggy wheels and your kids shoes too!). I like it but it sounds like a lot of work! You have to create a data base first, which means cheek swabbing all dogs in your area. I'd say the main culprits don't shit in their own neighbourhood. What's more, it also states that poo testing is not always reliable, I'd say because you'd need to find a rather fresh dog turd to test. But hey, whatever flicks your bean!