Adam Neumann was flying high. Literally.

His office-rental giant WeWork was months away from being valued at $47 billion. Revenue was doubling annually. And Mr. Neumann was zipping across the Atlantic Ocean in a Gulfstream G650 private jet with friends last summer, smoking marijuana.

After the group landed in Israel and left the plane, the flight crew found a sizable chunk of the drug stuffed in a cereal box for the return flight, according to people familiar with the incident. The jet’s owner, upset and fearing repercussions of trans-border marijuana transport, recalled the plane, leaving Mr. Neumann to find his own way back to New York, these people said.

Since Mr. Neumann co-founded WeWork—recently renamed We Co.—with Miguel McKelvey nine years ago, he has led with unusual exuberance and excess. His combination of entrepreneurial vision, personal charisma and brash risk-taking helped the company surpass $2 billion in annual revenue, and made it the country’s most valuable startup.

Now many of the same qualities that helped fuel his company’s breakneck growth in the private market are piling up as potential liabilities as the company prepares to go public—helmed by a CEO who looks little like a typical public-company chief.