When does a stock-market drop become something that poses a broader risk to the financial system?

In general, it’s good to remember the motto of Paul Krugman (Yale College ’74, incidentally): “The stock market is not the economy.” The stock market can fall a lot before we have to worry about broader risks to financial stability. We are nowhere near having to worry. Even if the market gave back all the gains from 2017 (another 25%), I would not be worried.

What should regulators be watching for as volatility increases?

Regulators need to pay more attention to the bond market than to the stock market. If seemingly “safe” bonds start to look risky, then we can have a problem. Risky things—like stocks—can be very volatile without troubling regulators.
Are you surprised that the current downturn has been so global? Why do you think that is?
The major stock markets tend to move together. Companies and macroeconomic risk are global, and big stock-market moves in the United States tend to go along with big moves in Europe and Asia, no matter which one moves first.