It's a pity investors bailed on the project, it seems like it was well ahead of its time, prototype failures are usually experienced behind the scenes, not in front of an audience that large and I think that they investors probably were on the money pulling out because of public perception, even if they blamed the tech, it was not the wheels that had anything to do with this, but more likely a lack of reinforcement of the main structure of the car.
As for flywheels: http://afstrinity.com/ that company (a merger of American Flywheels and Trinity Power) is probably right at the cutting edge.
Anything storing a significant amount of energy is prone to accidents, from batteries to rocks on the tops of mountains.
Flywheels are one of the few technologies that can store signficant amounts of energy and can be engineered to fail with relative grace, as opposed to say a fuel tank blowing up. Another strategy is to use many relatively small flywheels in parallel, each in their own containment vessel.
This also helps with some other engineering difficulties involving flywheels. Flywheels are ancient tech, at least 50 years old but probably much older, and if you count them as storage devices in a purely mechanical context as well then you can go back in to history quite a bit, about a thousand years.
For the obvious reason why 3 wheel vehicles have never become mainstream.... If you work with computers you should know about Single Point of Failure. If you are cruising on the highway and get a flat with 1 of your 4 tires it's no Big Deal. How do you think that would figure with only 3.
Or another example. Why so many wheels on an 18-wheeler. Wouldn't it be awesome if a truck could do a u-turn in it's own length? Those things blow out tires all the time. But it doesn't matter because they have 18. SPOF. 3 wheel vehicles will never catch on in the mainstream. They'll only ever be the equivalent of glorified motorcycles - the ultralights on the road.
The tadpole configuration has stability issues though, rolling it over is fairly easy if the vehicle has a high center of gravity.
The Reliant Robin solved that for the most part by reversing the arrangement putting the single wheel in front, but they still tend to overturn quit easily.
The accident mentioned above during the demonstration probably really was caused by that other car, but the ease with which a three wheeled configuration turns over most likely contributed to the severity, and in the long run would have had to be solved using tricky engineering such as a single wheel for low speed maneuvering and two wheels for higher speeds.
Here is a Reliant Robin doing what it does best:
I think there is a topgear episode where they try to improve the Reliant Robin by putting training wheels on it.
And I feel I should point out that the accident of the Dymaxion was in a prototype with a canvas roof. The death of the driver is probably the main reason it was abandoned at the time, that's pretty bad PR-mojo.
It looks like they're 'pivoting' away from using flywheels in favor of ultracapacitors and Lithium-Ion batteries.
An older article on the topic:
What about 5000? http://en.wikipedia.org/wiki/Potter%27s_wheel