Is there concern about market stability, given the events of the past few days (the short squeeze)?  Yes.    

Anytime you have an improbable event happen in markets (like a short squeeze that takes a stock from $42 to $483 in five days), there is likely some damage that comes with it.  If counterparties (brokers and banks) were to begin fearing the creditworthiness of other counterparties you can quickly get destabilization across markets.  Long Term Capital Management comes to mind. 

LTCM required a $3.6 billion bailout coordinated by the Fed.  Yesterday, within hours Robinhood raised a billion dollars.  That's the difference of two decades.  It's the difference between a Silicon Valley darling and a stealth Connecticut hedge fund.  And it's the difference between the global liquidity environment of today, and 23 years ago.  

To be sure, it's an unstable country, and an unstable world. 

But remember, there were global crises in the late 90s (Asian Crisis, Russian Default, the blow up of LTCM), and yet it was a boom period for the economy and for stocks.  There were plenty of shock risks coming out of the depths of the financial crisis (near debt defaults in Europe, U.S. debt ceiling sagas, government shutdowns, Russia's invasion into Ukraine, nuclear threats from North Korea, the Ebola scare) … and yet the broad stock market tripled in five years. 

The shared feature in those cases: Intervention (or the threat of intervention). 

We've had plenty of intervention over the past year.  And we will have more, if needed, by central banks and governments to maintain stability.