Social inequity is the number one concern when it comes to stability in the PRC. Right now what you're seeing is a situation akin to the late 1920's in the US: rapid industrialization, rapid urbanization, a steadily rising standard of living (at least in the cities), and a relative handful of uberwealthy. Guys like Jack Ma are China's Carnegie/Vanderbilt/Rockefeller. As in the 20's, there's not so much a resentment of the uber-rich as much as there is an aspiration to be like that, and an enjoyment of this newfound economic freedom compared to rural village life (with a concomitant reactionary movement against it by those left out, and a nostalgia for "the old days").
Some major differences:
1. Religion doesn't play a role. You don't have fiery preachers railing about alcohol and flappers and "immoral lifestyles" in the cities.
2. The interethnic unrest of places like New York and Chicago doesn't exist because China's 98% Han. The minorities are mostly in their own provinces or subregions thereof. It's more like the reservation system in the US than the polyglot "melting pot" we're used to. Thus, any ethnic unrest is rather easily (and harshly) dealt with. And with the exception of the Uighur and Tibetans, the other ~50 official minorities aren't a problem.
3. The current (and hopefully future) leadership are technocrats, not ideologues. They believe in bending rather than breaking. If they see a major source of economic unrest, they'll take steps to mitigate it.
4. Corruption is a major problem as well (as it was in the US at the turn of...okay, let's just say forever). But there's a cultural difference. We have this weird notion ingrained into us from childhood that the Founding Fathers were all pure and noble and that government in the US started off perfect and it's only over time that it's gotten more and more corrupt. So we get angry.
China has been dealing with problems of corrupt governance for at least 3000 years. There's more of an implicit understanding that this is the natural state of things. They still get angry, but it's anger focused at the corrupt officials, not a "tear down the whole damn thing and start over" kind of rage that's so popular in the West. Yes, to be fair, they DID tear down the whole damn thing twice in the 20th century and at least a dozen times over the last couple of millenia. But there's an understanding that doing so means a LOT of people are going to die. Dynastic change is essentially the ruling agency being a phoenix, reborn in the ashes of its own funeral pyre. It's only worth it when the last incarnation is so sick, weak and ineffective that it's worth going through that violence. The current incarnation is nowhere near that sick, weak *or* ineffective.
I don't see it happening anytime in the next 10 years at least, unless the global economy just totally implodes so fast that it takes China with it. In which case, we'll all have more immediate problems to worry about.
EDIT: I will also say that I don't ever see China becoming a democracy. Ever. There are pro-democracy activists, but in my experience the vast majority of Chinese that I've talked to aren't particularly interested in political self-determination, but rather economic self-determination. If they can make enough money to get an apartment and a car and afford a child, they're cool with whatever. Perhaps at some point in the future when the "middle class" is large enough, there might be serious inroads in that direction, but even then I dont think it would be wise. I've long held a personal theory that there's an upper and lower limit on the population numbers where democracy works. China is simply too large to be an effective democracy. (I would argue the same thing about India....it *is* a democracy, and it's mostly ineffective at the national level. It only works by being a mostly decentralized federal system where the real work gets done at the state level).