I smell snake-oil. Something aint right. If it works as advertised, every automaker would be installing them. Thousands of engineers cannot be wrong, a couple here and there yes. But the majority (playing it safe, is probably an overwhelming majority) in an entire industry? Heres what I've taken notice on.
Gees, DGthe3
Are you surprised when the sun comes up every morning??? 
It is possible that they are telling the truth. Not everyone is out to scam the buying public. Hydrogen has long been proven in increase performance, reduce emissions and increase efficiency.
There are more then a few reasons why manufacturers don't want to accept the risk of installing a system like this in a car. For one, who knows what the liability and engineering costs would be to safely create, store and introduce hydrogen to existing air/fuel systems.
Plus, the news station put in on a Dyno. Watch the Vid on the news page, top right hand side.
I'll admit the web page is weak at best, and there are a lot of websites selling you instruction manuals on how to build this system when the information is readily available for free on the web. Doesn't mean it doesn't work as advertised.
1) patent pending. Patents can only be approved if the thing does what it says. So long as they are applying for a patent, it is patent pending. That does not mean that it will work. Doesn't mean it won't work either. Just something to look out for
Fair point
2) Anything that I have heard, nearly all of these systems are a scam. A select few aren't. I haven't found anything on their web page that describes how their system works. They explain about electrolysis and other things, but nothing specific to how they get such improved fuel economy. That sets off warning bells in my head.
Electrolysis is how they make the Hydrogen. Which is then introduced into the Air intake. Similar to NOS but it is always on. The Hydrogen Allows the combustion chamber to burn almost 100% of the fuel vice approx 85% without the hydrogen. Hence, all the benefits.
3) Where are they getting the energy to run this thing off of? They say themselves that electrolysis is 50-70% efficient, ignore the theoretical limit stuff. That means that roughly 1/2 the energy you put in actually goes into getting hydrogen out. Then there is the pesky problem that it takes more energy to break the hydrogen-oxygen bonds in water than you get back from them when the reform under combustion, not sure of the exact numbers but I think its something like 75% but that is little more than a guess. Then, figure that the infernal combustion engine is roughly 35% efficient when burning gasoline. Finally, I think its safe to assume that the juice to run it comes from the alternator in the car, which runs at about 60% efficiency. So, for every 1000 units of electrical energy that gets put in, you can expect at most 110 units back, possibly half that. This is why hydrogen is not a fuel source! Would you believe someone that says that it is a wise investment if you get a dollar back for every 10 you put in?
Have you ever been accused of over thinking something? It's driven by the electrical system and it takes far less power then the radio. More like a few cabin lights.
Based on your interpretation of the power required vs the output of the system, the car would perform worse with this system since it takes more power to run than it creates. Watch the Vid. They proved it works. So in the end you believe them or you don't. I'm quite certain your analytical mind can grasp that if you improve efficiency you will decrease expenses over time. You will recover the cost of the system and spend less on gas as long as it never costs more to maintain and run the system then it does to buy gas.
Based on that, unless there is some sort of special effect of combining hydrogen with gasoline that makes the entire process more efficient (it happens with low amounts of ethanol so its possible), it is impossible for this to improve fuel economy. It merely creates a drain on the battery and alternator. I am not a combustion expert, but I would guess that this device does 1 of 2 things. It will either add oxygen, venting the hydrogen gas back to the atmosphere. That would allow for more complete combustion to take place, reducing the amount of unburned fuel as well as carbon and carbon monoxide gas levels as well as several others. I think this may be the case, not positive though.
You're just plain wrong here. the system is designed to remove oxygen from water so you are left with hydrogen. It injects the hydrogen into the air intake. This is what allows it to burn nearly all of the fuel in the combustion chamber.
The other thing that may happen is the hydrogen burns hotter (or possibly cooler) allowing for a different set of reactions to take place. This would make for the lower emissions levels claimed. No idea how it improves economy.
I don't know for sure. My guess is it burns hotter if it's burning more fuel in the same volume combustion chamber. However, If it burns more quickly then the engine won't have a residual heat problem.