Fundamentally, we already have self-replicating robots with nano-level structures that consume materials from their surroundings and build new copies. They're called bacteria. The interesting bit over here is not the observation, but the question why we aren't all covered in bacterial goo miles thick like run-away nano-technology. (we do have them all around us and in us for what its worth)
I think a part of the answer is that if you have free form replication that isn't perfect, then sooner or later something is going to emerge from that goo that realises that it's just more efficient to eat the goo. Combine that self correcting cycle with hard limits imposed by nature (presumably they need to have a power source to make it work - the goo would start to die the minute it gets to a millimetre because of inaccessible sunlight. Then there is toxicity, what happens to the waste? Heat dissipation. Structural issues and other things...) and you have the recipe for a shorter sci-fi series than Firefly. (Dear Mark, today we succeeded in making self replicating nano-robots. They were exponentially multiplying within the petri dish and then they stayed in the petri dish, because apparently nano-robots are tastier than glass and metal. Doesn't matter though, we cracked open the crate of champagne anyway.)
Which is also an argument against von Neumann probes, btw. Perfect replication isn't possible, so sooner or later you are going to see a ton of weird errors accumulate to unpredictable behaviour... (perhaps a shark that goes around "eating" other probes?)
Bacteria aren't capable of spontaneously organizing into multi-celled organisms when they reach critical mass.
Fungi behave much more like this. The thing we don't have an example of in nature is an intelligent creature capable of making tools that can reproduce itself from a single cell. It's definitely a hard engineering problem, but it's conceivable. It's also conceivable that such an entity could seek out and remove any malfunctioning sub-entities.
We humans actually behave a lot like that, it's just that you need at least a whole human to grow another human. It's not so strange to imagine a designed, intelligent creature that can regrow itself from a small piece.
Viral capsids are an even simpler example of self-assembly. In many types of virus, the individual subunits spontaneously piece together to form the capsid in an entirely passive process driven only by Brownian motion, and defined by the chemical composition of the subunits and the solution they are contained in.
Evolution isn't likely to happen in self-replicating robots. Evolution needs a continuous fitness landscape like DNA. A random bitflip is more likely to produce a fatal error than do something beneficial. Even worse if the code is encrypted before copying. There also aren't that many generations. At exponential growth, it only takes a few dozen generations to reach the maximum population limit and stop replicating. Not enough generations for evolution to happen.
Obviously the technical issues with self-replication are difficult, but nature was able to do it with relatively crude methods. No doubt we could eventually design something significantly better. One major advantage would be mass cooperation. Evolution has no incentive for individuals to cooperate with each other, but designed nanobots can specialize and benefit from economies of scale.
Multicelluar organisms exist but they aren't "fluid" like I described. It's not like animals will spontaneously combine into a single organism. Some plants can sort of do this, like bamboo forests. But they don't have a lot of specialization like animals do, with different organs and stuff.
Your analysis ignores the key point that bacteria operate on simple rules based entirely on local concerns, which is not the proposed case in the sci-fi story.
So you're saying that top-down management or even peer-to-peer management will exist within the grey goo scenario? I'm somewhat skeptical about top-down management, as there would be enough nano-bots within a 1cm deep layer in a city the size of NYC to far outstrip the attempts of a complex entity to control them coherently. As far as peer-to-peer communication goes, then bacteria are already doing this; http://www.hhmi.org/research/cell-cell-communication-bacteri... and they still haven't covered us in grey goo.
I think a part of the answer is that if you have free form replication that isn't perfect, then sooner or later something is going to emerge from that goo that realises that it's just more efficient to eat the goo. Combine that self correcting cycle with hard limits imposed by nature (presumably they need to have a power source to make it work - the goo would start to die the minute it gets to a millimetre because of inaccessible sunlight. Then there is toxicity, what happens to the waste? Heat dissipation. Structural issues and other things...) and you have the recipe for a shorter sci-fi series than Firefly. (Dear Mark, today we succeeded in making self replicating nano-robots. They were exponentially multiplying within the petri dish and then they stayed in the petri dish, because apparently nano-robots are tastier than glass and metal. Doesn't matter though, we cracked open the crate of champagne anyway.)
Which is also an argument against von Neumann probes, btw. Perfect replication isn't possible, so sooner or later you are going to see a ton of weird errors accumulate to unpredictable behaviour... (perhaps a shark that goes around "eating" other probes?)