China's rise is a commonplace of our times. The last major state on earth ruled by a Communist party appears set to dominate the planet, surpassing an anaemic west and owning the 21st century. After the temporary economic downturn of 2008, its growth has soared once more to make it the planet's second biggest economy. Everything about it is huge, starting with its 1.3 billion people. Its Communist party is the planet's biggest political movement; it contains 55% of the world's pigs; its people smoke 38% of the cigarettes consumed on earth.

So it is very easy to be swept away by the apparent inevitability of China's dominance, especially for those who were let down by the Soviet Union's failure to get the better of the United States and now see a new champion in the east.

The reality is that, as it prepares for a wholesale change of leadership starting later this year, the People's Republic faces fundamental tests which will determine if it is able to continue its upwards trajectory or will be caught by the deep flaws in its system – political, economic and social.

The political scene has been enlivened this spring by drama surrounding Bo Xilai, the rock star of Chinese politics, who crashed to earth amid murky events in the mega-municipality of Chongqing, which he had made the launching pad for his ambitions. But the real challenge for the leadership goes far deeper and starts at the very top of the system.

The Communist party's monopoly position means that it and the government which comes under it dominate the economy and society as well as politics. But what is it for? Is it merely a managerial elite relying on growth for legitimacy, defending the status quo on behalf of those who have profited from economic expansion?

Hu Jintao, the Chinese leader who will step down at the next party congress, probably in October, preaches the virtues of a "harmonious society", evoking Confucian virtues. Yet wealth distribution is more unequal than in the west. Materialism rules, epitomised by the young woman on a television dating show who said she would rather cry in the back of a BMW than laugh on the back of a bicycle.

In the opaque world of top-level Chinese politics, we have little idea of what Xi Jinping, Hu's anointed successor as party secretary, stands for. Asked how he got to the top, sources in Beijing reply that everybody is comfortable with him. We know that he belongs to the so-called "princelings group", the offspring of first-generation Communist party leaders, and rose through the party ranks in booming east coast provinces before being elevated in 2007 to the standing committee of the politburo, the supreme decision-making body, in a closed-door process at the five-yearly Communist congress. We know that he has enjoyed the support of the "Shanghai faction", which used to run China and is well-connected with fellow princelings and younger generals in the People's Liberation Army. But nobody knows what his policy preferences are and, I would guess, he has not decided them himself, waiting like the canny politician he is to see the balance of power in China after he takes the top job at the party conference later this year. Hardly the recipe for grappling with the major changes China needs.

The economy is, as the leaders acknowledge, seriously unbalanced, with excessive dependence on investment in property construction, infrastructure and exports. In this nominally Communist state, the share of wages in national income is far lower than in developed capitalist nations; the forces of capital have been the big beneficiaries of growth, not the workers. People are registered to their place of origin and so migrant workers in cities lack the right to education, healthcare or property purchases. An effort is being made to boost blue-collar pay and thereby stimulate consumption as an economic motor, but this will be, as a party school official told me, "a matter of two five-year plans".

China wants to move up the technological value chain, but it is not clear that it has the skills to do so. Training takes time. Top jobs in the huge state sector are decided on political grounds as well as competence. The drive to do everything bigger and faster than anywhere else showed its limitations with the crash of a high-speed train last summer, killing 39 people.

There is a huge environmental crisis. northern China is seriously short of water. Agriculture is hobbled by a multitude of small plots leased from the state that cannot support mechanisation. The "demographic dividend" of young workers is about to fade as the result of the falling birthrate, while improved healthcare means the number of people aged over 60 is equal to the population of Spain – that in a country without a proper pensions net and where the traditional family structure is strained.

Underlying everything is a serious trust deficit. "Only believe something when the government denies it," is a common saying. Corruption is endemic, accompanied by lack of accountability and weak rule of law – judges have just been told to swear a loyalty oath to the Communist party. There are recurrent food scandals; cartons of UHT milk from New Zealand sell for several times the price of domestic milk because people think it is safe.

While individuals are far freer than in the days of Mao Zedong, any form of organised dissidence is ruthlessly crushed – the budget for internal security is greater than that for the armed forces. Still, there are reckoned to be 150,000 popular protests a year, some involving tens of thousands of demonstrators. Society is evolving at breakneck speed. Social media make the control ethos embedded in the party's DNA increasingly difficult to implement.

Despite all these fault lines, China is not going to collapse; it is far too resilient for that. Its growth has made more people materially better off in a shorter space of time than ever before in human history and this breeds loyalty to a system. But two things are clear. It does not provide a model for the rest of the world as its admirers might wish, and the danger now is that, unless Xi Jinping and his colleagues in the new politburo undertake serious reform, China will be stuck in an increasingly outdated groove, out of tune with its needs and aspirations.

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