Jellyfish are not active swimmers--they ride whatever current is in the water. In square tanks, this causes many species to get stuck in the corners where the water is stagnant.
Also, this means that they can't fight the current and generally get sucked into the filter intake. At the same time, they need strong current (see the comment about them getting stuck in stagnant areas) so you need a filter with a strong intake.
Some species, like moon jellies, all you need to do is diffuse the intake. You can see a section in the video where in the background they demonstrate a filter with the intake buried under a layer of marbles.
For other species, you need a specially-shaped tank called a 'kriesel'. (Do an image search for 'kriesel jellyfish' for some examples.) These tanks are shaped like a hockey puck standing on its edge, and move the water in a circle, so that no area is stagnant. Also, a water current blows across the filter intake, so the jellies get pushed aside instead of being sucked in.
Fun fact: The big jellyfish display tanks in Monterey Bay aquarium are actually oval-shaped kriesels with current blowing down both sides, and back up the center. That's why the jellies always seem to be upside-down--they're facing into the current in the center of the tank. :-)
I'd also disagree with the claim that jellies don't need any "exotic care": They're physically very fragile, and you have to be very careful to avoid damaging them when you clean the tank. They also require special food (notice that you're supposed to order special food from this guy) and high water quality, not to mention the special tanks already mentioned.
"Never gave any thought to having a jellyfish as a pet. I'm kind of a furry animal guy - dogs and cats and what not"
This isn't meaningless. People who had never thought of having a jellyfish might read this and become curious. In fact it sounds like pretty good PR, considering it's just a news story.
It does sound like pretty good PR (which is great thing for Alex and his company), but pretty poor news.
Imagine if they'd interviewed a marine biologist about this species of jellyfish instead? It would have been even better PR (expert confirms they don't sting, are abundant etc), but it didn't happen because it's always easier to ask two people in front of the ABC building what they think.
In some strict sense it is not devoid of meaning the way colorless green ideas sleep furiously, purple monkey dishwasher is, but if you have sufficient experience with human culture to understand the article at all then it doesn't tell you anything you don't already know; people typically don't consider jellyfish as pets.
Perhaps a combination of those "AeroGarden" devices that let you grow fresh veggies and herbs, and one of these jellyfish setups with edible jellies, and you could have your own fresh sushi source (just add rice)!
http://www.nytimes.com/2009/03/14/technology/start-ups/14sta...
I'm wondering how long these marvellous creatures will survive in your tank if you treat them well.