What they describe is essentially forward error correction so packets do not need to be retransmitted but it adds overhead to the steam. FEC is already common on many of the lower level protocols that are in use but adding it to routers at the IP layer seems like a bit of a step back.
With IPv6 routers no longer perform packet fragmentation for instance because there is a need for them to be faster/dumber/ cheaper. Out of sequence packets are generally fine with TCP because the packets are each numbered for reassembly.
Data could be sped up essentially by rolling CDN functionality directly into the protocol (today it is mostly a feature bolted on to DNS). Hosts can be assigned a CDN node through DHCP option 82 and send reference it with their GET request, the server then points them to that CDN and the client reports performance statistics back to the centralized controller for monitoring. It saves the trouble of having to know the location of all the caching DNS servers doing lookups to guess which cluster to serve the client out of and you can always still just point the client request elsewhere if there a reason to (like degraded performance).
This wouldn't be terribly difficult to deploy into the protocol but I believe Verizon and some other people own patents that would prevent it. Thankfully some of those patents are nearing their lifespan.

GREAT—let me know how it works out for countries outside the US!
The notion that free market increasing competition and lowering prices in the US is a lie at the Big Corporation level. Look at other markets, like cable/data services. The companies don't compete against each other, they just quietly collude to set up fiefdoms around the country like a bunch of mini-monopolies, thereby keeping prices high and those huge bonuses coming in for the executives. There are HUNDREDS of examples of less gigantic companies (with less lawyers, resources and Congressional clout) where companies are found guilty of collusion (essentially conspiracy) and they just quietly pay their fines and then try and find another way to game the system. Monsanto and Japanese agribusiness chemical suppliers and recent flatscreen manufacturers come to mind—WE NEED STRONG WATCH DOGS TO PROTECT CONSUMERS—AND GOVERNMENT OFFICIALS NOT OWNED BY THE CORPORATIONS THEY'RE SUPPOSED TO REGULATE.
According to Pulitzer Prize winner Investigative reporter David Cay Johnston, author of "The Fine Print.":
The Internet was invented in the U.S., but we've fallen behind other countries in terms of access and speed. Our service is more expensive than in any of those countries. Why? Wealthy corporations have worked the regulatory system to their advantage to their benefit so that the fees that banks and phone and cable companies have added over the years that have made your bills incrementally larger but have added up to big money for corporations.
Through various fees above the stated cost, in our phone bills, we've actually been paying, over the years, to create the cable network that provides Internet access and cable TV. We've paid, between cable company rate increases and telephone company rate increases, over a half-trillion dollars to get the Internet.
Per bit of information, we pay 38 TIMES what the Japanese pay. The US now rank 29th in the speed of our Internet, according to Pando Networks. We're way behind countries like Lithuania, Ukraine and Moldavia in the speed of our Internet.
American triple-play packages average about $160 a month, including fees. The same service in France is only $38 a month with an Internet that is 10 times faster uploading - downloading and 20 times faster uploading, with much broader international television stations than you get here.
Thanks to our donation/payola loving local, state and national elected officials, US consumer now dance to the tune of our corporations—NOT the other way around.
This country may have once been the envy of the world, it's a sad, corrupt place now.

There was another project that was really interesting, the idea was to turn the whole interenet into a mesh network. I think maidsafe was the name of it.. Really interesting for further reading.

Bogus. Internet speed is constrained by switch processing power, not packet paths etc - this uses *more* switch processing - put this on a real internet, and the net result is going to be a 10x speed reduction. (it's a no-starter anyhow, the CALEA law makes this idea illegal to begin with).

First false premise is that packets need to be received in order. This is not true for TCP. That's what the receive window is for. Packets can be received in any order within the window. Selective acknowledgements assist in efficiently requesting resends where a packet was actually dropped due to congestion.
This proposed method sounds like just another compression algorithm. It will also suffer from dropped packets. If it doesn't, it would have had to bloat out the payloads to provide redundancy. You can't get something for nothing.
As for storing data in the nodes.... well since the "node" is a router, I don't think that will happen any time soon.

@yrag people point out the cost of Internet in other countries mostly ignoring that a) the US has a much lower population density than most countries and b) most goods and services no matter what they are are generally more expensive in the US than around the world because its a different economy. Japan has 10x the population density of the US. The average household income in Ukraine is a fraction of what it is in the US.
It's true the executives are making too much money but that's also true of most public companies. After calculating for other factors like population density and economy I might still pay too much for Internet but the difference is likely a miniscule percentage of our yearly budget, its really amazing how much mental energy people spend complaining about it.
People pay half their income in taxes and still have to pay out of pocket for things like education, healthcare, and retirement. Middle class housing in some areas is anywhere from $250k to $1,000,000 and some people come out of college with 100k in student loans to pay back but what matters is the ~$180 you could save in a year by paying $15/month less for Internet access. If it was really that profitable more companies would be coming up with the money needed to enter the market or expand aggressively. There are a lot of costs associated with new deployments and it takes a long time to realize the investment of building out.
@christopher A half decent read is http://en.wikipedia.org/wiki/IPv6#Simplified_processing_by_routers Essentially things like packet fragmentation, checksum, and queue timers are removed from IPv4 to IPv6. Checksum was purposely removed because its a redundant function with lower layers of the IP stack. IPv6 also uses a simplified fixed length header. It's expensive to run routers with a lot of features and processing power when you mostly just need them to move a lot of data cheaply and efficiently.
There is a huge difference in cost/bit for optical transport hardware vs router hardware in part because transport can just dumbly push on the data without having to do computationally expensive work like reading packet headers along the way. Facebook, Google etc. are frustrated with router costs and have taken to rolling their own (SDN based) routing platforms to force down costs. Another example of this was the industry move from SONET based circuits to cheaper ethernet based circuits/hardware.
There are better solutions to the problem than this (like pushing content delivery storage closer to the edge). There also isn't much need to send an existing TCP packet flow over multiple physical paths because routers have thousands of data transfers at any given time and they can just load balance per flow to achieve utilization of another path without having to subject individual flows to jitter.
Don't get me wrong, there is nothing wrong with new ideas and an outside the box look at the problem but I don't see it as a viable solution.

yrag is correct that we need watch dogs, but just dreaming to believe the bureaucrats will EVER not be "owned" by the industry. The corporation has the time and resources to focus on their particular regulators, while the poor consumer has to divide his attention among the bread, car tires, roof shingles, potatoes, shoes, and everything else needed/wanted for modern life. The regulate-everything mind set is how we got into our present situation.
The answer will be complex, but the principle is simple: limit the involvement of politics as much as possible.

If yrag can show me one example where govt. was not corrupt out of the last 10,000 years, I would not quote Einstein to him: "Doing the same thing over and over while hoping for a different result is insanity."
piper Tom: "... as much as possible ..." is correct. When people are willing to give up the worship of rulers, i.e., so-called leaders, as a viable social system, then we can begin to use the newly freed up market to provide security. It will quickly be realized that it was always "possible" to live a civilized life without being controlled, and be more prosperous.
We don't have to fear self-governance any more than free markets. You can't have one without the other.

Great, but the NSA would never allow it.

Another thing they seem to have totally ignored - the quality of the connection. Actual physical connection is the limiting factor just about everywhere - for example, if you are at the end of a 7+ km very crappy coper line you are not going to get much more than a 1mbit connection, if, on the other hand, you are sitting on a t1 line then the sky is the limit. In the first case no matter what you do to the packets you are not going to get a faster connection, in fact the system described would most probably cause a SLOWER connection because of increased resends.