Don't forget that Communism is (per wikipedia)

an ideology that promotes the establishment of a classless, stateless social organization based on common ownership of the means of production.

I would argue it's never been tried: what we got was State capitalism.

I'd say that the ideology has indeed been tried, and what it created (necessarily, if it was to create anything but talk?) was state capitalism. Here, of course, rdf's distinction between capitalism and markets is a crucial to the way the terms are being used.

Words and ideas I offer here may be used freely and without attribution.

For example, government participation would certainly influence the job market - entrepreneurs might not like that, but if the society acknowledges that there is power disbalance in employment negotiations in emphatically "free" markets, with unfair disadvantage for workers, why not have a market player (government) which would not be primarily interested in making labour force cheapest possible? Private companies would have to compete with government for qualified (and even unqualified) labour, and perhaps cumbersome regulations of employment could be greatly simplified.

The modern practice of contracting private companies for every public errand adds a bureaucratic layer, is often wasteful and corrupt, and benefits just a small group of owners and managers of the contracted company - how is that better than letting government manage basic services and jobs itself?

Government companies would set standards of key services. Private companies would always do better?? Great!! Let them have their better ideas and implementations, compete with themselves and the dumb government. But services should be kept not only for those who could spend most, but for everyone.

Would competition in market sectors with government participation be unfair (to enterpreneurs), compared with the competition with no government participation whatsoever? Well, is competition with Wall Mart fairer?! Government companies might deliberatively leave niches for competitors - destructive monopoly is not their aim. Markets change so fast and radically (LPs replaced by tapes replaced by CDs then DVDs, etc), that it is hard to tell what is fair.

Certain inertness of the government might cost a little, probably impede front innovators somewhat, but its relaxing social influence could be valueable. Does a society has to run headlong together with every trendy innovation, regardless social and economic risks?

How to define what services are up to government? Well, there has to be no Bible what the government has to or does not have to do. As times change, social preferences and imperatives may change. Some services might be discarded or privatized, some new engagements could be started. If monopolies must be controlled in ways that bring them very close to state ownership anyway, why not have straight state ownership, or state competition?

As for decision mechanisms, they are not set in stone either, though democratic principles and public influence could be a basis. My suggestion is that decision committees are formed from the public (like with trial juries), and each citizen could be employed in these committees strictly temporarily. Possibilities are ample, I think.

Here's another possible government strategy: To facilitate innovation and reward of real innovators, there would be governmental research institutions, where research (especially of socially desirable innovation, like alternative energy) are supported by government, and researchers with great results would be given a chance to start their own businesses. These researchers could also be educated in marketing and similar things, if desired. In this way, really bright innovators would run less risk of failing to introduce their innovations into the market because of zero inadequate business understanding. The investor class would be somewhat disadvantage, but do they really deserve the monopoly of knowledge how to operate in the markets? Why the society has to reward primarily those who know that one thing of running a business well, when others without that knowledge or emphatic interest have little chance to earn a million?