The problem is when people make a bet that doesn't work out. There are a lot of exotic trades that can clean you out completely in an instant if you bet wrong.
I wonder how Robinhood will handle it when it happens.
From http://www.investopedia.com/terms/m/minimummargin.asp:
"When you buy on margin, there are key levels - as governed by the Federal Reserve Board's Regulation T - that must be maintained throughout the life of a trade. The minimum margin, which states that a broker can't extend any credit to accounts with less than $2,000 in cash (or securities) is the first requirement. Second, an initial margin of 50% is required for a trade to be entered. Third, the maintenance margin says that you must maintain equity of at least 25% or be hit with a margin call."
Of course, should Robinhood go under, don't expect easy access to your assets, until some other brokerage takes it over.
The gigantic risk to Robin Hood isn't that they'll have problems collecting occasionally. They can make up for that by fiddling with their fees to come ahead in the average case.
It's that some big market move busts everyone at once and they go bankrupt overnight.