A whole anarchist society?

Here you ignore basic Marxist theory. The working class (proletariat) will be the ones who engage in the revolution, for they are the exploited and those who must seize hold of the means of production. Hence it is impossible to "organize" a whole city, country, etc... without class consciousness on the part of the workers involved.

If each center of production is run and controlled by the workers themselves, these workers can then communicate with other centers of production to coordinate whatever is needed. Furthermore, it is assumed within the context of a revolution that economies will be highly de-centralized, thereby making the 'problem' of distribution null.

Why is there crime? Because people don't have what they want. Given that anarchist/communist theory is a movement towards a society based around the principle of 'to each according to need, from each according to ability,' this problem will not exist. But even if there is crime, why would you require others to deal with problems in your local community? Are you and your community not capable of handling your lives yourselves?

Infrastructure is dependent upon the workers who allow it to be constructed and maintained. If the revolution were to occur, these people would be in charge of the infrastructure, thereby leading it to be improved due to the absence of exploitation and disassociation of labor.

Anarchism and Communism are practically identical. They differ on the sole issue of the 'transitional period' between capitalism and communism (known as 'socialism'). Aside from this, they share they same values of freedom and equality, oppose the same economic system of capitalism, oppose the same cultural/social systems of inequality, discrimination, and subordination, and work towards the same goal (a society based around the principle of need/ability).

- August

It seems you've fallen into a productivist trap. Productivism is an empty philosophy that is nowhere near as utilitarian as it would seem; it mostly results in a waste of resources on huge amounts of useless goods and generally relies on poverty to do so.

Direct democracy doesn't preclude collective action against those types of crimes which will occur in any society, and that the vast majority of criminal behaviour is either a direct product of capitalist culture (most property crime) or is only really criminal because the state defines it to be.

I really wouldn't say that, it's just that you have some examples from state communism of a communist economy in practice. Communist in name, at least. If you really think about the economic theories and models that were in place prior to the emergence of capitalism or state communism, there wasn't a body of work any more involved or complex or unitary than what is present in anarchist literature - it's not like reading Adam Smith is going to give you a blueprint for a capitalist economy, or indeed, much more than a justification of the market based on its mystical properties, by which it's "magic hand" will make everything work out for the better.
Anarchism can - and has - organized real-world economic systems which provided for the needs of a populace, in the few instances it has briefly surfaced such as Spain or the Makhnovshchina. Like capitalism or communism, economic organization didn't emerge from theory so much as from situation and practice. Generally its problems lay in its inability to resist incursions by conventional military forces, but arguably, the battlefield has since changed to favour small actions and more decentralized and redundant forms of organization. A recent example among many:

Israel has defeated larger Arab armies repeatedly since its creation in 1948. The Israeli Defense Forces (IDF) enjoyed a reputation of invincibility among its Arab neighbors until last year. Israel got bloodied and bogged down in Lebanon by a stateless military organization: Hezbollah's military wing, the Islamic Resistance (IR). The Israeli high command expected the air force alone to crush the IR. Instead, the air force killed many civilians and destroyed property but could not stop the IR rockets and missiles that rained daily on Israel. When IDF troops tried to push their way into a well-prepared defense, they failed. It seems that the Israelis have lost their ability to conduct high-intensity maneuver warfare. (from Infanty Magazine)

Name one.

There are lots, and many have been around for ages ... the aynuqa system in native communities in Peru, though it exists in the context of a capitalist state, is more or less a system of direct democratic control of land and resources, and a mix of usufructuary and collective property.

Productivism is, basically, the idea that more production is always good.

Lacking a productivist mindset doesn't necessarily mean that one denies that the fruits of production can have value, it simply means that one denies production itself has any value - production is a process, not a goal. Having enough food or shelter for everyone is a good thing, but this isn't what productivism is about. Productivism is a form of process worship, where the method is blindly valued over the outcome. If greater production can be obtained by assigning land that could be used for food or shelter, to the production of, say, fibres to be used in the manufacture of unnecessary, disposable packaging, then that is desirable according to productivist doctrines.

To give a very common example - let's say a company designs some new product. It is produced by means that have an externality cost, in terms of damage to the environment. It is found that demand for the product is very low or nonexistant, even among consumers who have seen or heard of the product. So the company expends more resources on advertising to generate demand that never existed. It employs television, eye-catching packaging and so on to make the product more enticing. Demand fluorishes and so production rises. Supposedly, according to productivists, value has been increased and wealth has been generated.

But the productivist doesn't like to look at the externality cost. The environment is being damaged. This has real inherent value - it sustains life and enhances the quality of life. Value is being diminished, which is a cost even though it is not represented in the value of the product itself (an externality cost). The product itself has no inherent value at all - demand for the product had to be engineered, so there is nothing inherent about any value assigned to it. Productivism trades away things that have real, inherent value for things that have no inherent value at all, because it blindly worships the process of production, without regard to outcome.

Our economies are filled with useless products and millions and millions of workers are employed in work that they instinctively know is utterly useless and has no real value - very few people in call centres or working the floor at Wal-Mart actually feel they are doing anything of importance or value, it just pays the rent because of the way productivist economies distribute wealth. We've long surpassed the productive capacity to meet needs, heck, we've passed the productive capacity to meet wants - we must now employ advertising to generate wants which never existed. And we're destroying the environment, depleting natural resources, diminishing the quality of life with billboard eyesores and contaminated air, bankrupting future generations and denying billions access to basic needs, just to meet these engineered wants - a direct result of the productivist mindset. Yet still more production is deemed a good thing - even if it produces goods that have no inherent value at the cost of life-sustaining things that do. This is why blind productivism is a problem, especially today.