Contradictions don't end with socialism. One ruling class, the proletariat, does not mean society becomes a homogeneous body, walking in one straight line on the yellow brick road to communism. There will still be just as much debate and tumult over how the new society should be run. First you have to contend with the fact that the majority of the populace will not be communists, so you will have to apply a mass line so the average person is routinely exposed to communist political thought. Then there are the divisions between physical and mental labor within the working class. The contradictions between the proletariat and the lumpen-proletariat (thieves, beggars, and soldiers). Then the division between administration and working class. The resolution of these contradictions will be resolved through conflict, probably even violence. Even the concept of the withering away of the state will not happen in one easy motion. This will be bitterly fought over. What is to be done is institutionalize radical measures that creates equal control of society between the administration and the people. If you have a society where the administration has total control, this will regenerate class distictions. If you have a weak central body where workers just manage themselves this all regenerates class distinctions.
The administration/government are not the same as the state. The state is armed bodies of men, the legitimate armed force in any region. This includes jails, courts, police, and the military. The state exists solely as a tool for one class to suppress another. If the bourgeoisie no longer exist, and we have overcome class distinction and the social conditions that create them, then what will be there for? As for the administration, that probably never disappear all together. It must necessarily be embedded into production, and have a good measure of control over it's workings. This is necessary for a planned economy. How do you drive a car with no steering wheel? How can plan an economy with local soviets? How can you move society in the direction of communism, a classless, stateless, moneyless society with worker's direct democracy? It not only impractical, but will never overcome the social conditions which generate class distinctions. An administration will probably always be necessary in one form or another, but as the material conditions change, so too will the nature of government. The more the workers learn more about communism and the direction we are trying to go, they will take on more of the work the administration use to do. Again, society is no longer run in a way where everyone is competing for work, we are trying to eliminate that. Everyone does what they do because they want to, fighting for the means of subsistence isn't the reason people work anymore. And no one is an administrator for long, it will change all the time. So what does the particular person care if they don't get to be part of the administration anymore? Get a new job, any you want, we have universal employment! These things will disappear for the same reason everything else does, the conditions that created them will no longer exist.
As sanpal said, capitalism and the capitalist mode of production are not the same thing. It is a capitalist communist sector, because it is a capitalist mode of production run on the communist economic model. We will still have things live "wages" and "capital" and "a market". They will not exist in the same sense at all, but will be similar phenomena operating in generally the same way. But they are still antagonistic to socialism, and will have to be broken down. This can never really be done without international socialism. And yes, this is similar to the soviet model. We will necessarily have to take aspects of the soviet model, but of course not all or even most of it. Take the good, leave the bad, do better next time.