Boeing Co.'s incoming boss David Calhoun faces a daunting task when he takes over as chief executive officer next year: rescuing the 737 Max while mending the company's fractured relationship with U.S. regulators. But that's just the first of the hurdles awaiting him.

Calhoun, who takes the reins Jan. 13, will be leading a once-proud company whose reputation for engineering prowess is now in tatters. On top of the grounding of its bestselling plane after two deadly crashes, Boeing has suffered production stumbles with its KC-46 tanker, delays to its 777X jetliner and an embarrassing mishap that caused its new space capsule to miss a rendezvous with the International Space Station over the weekend.

Then there are growing signs that jetliner sales are cooling after an unprecedented 15-year boom. And the aircraft demand that's left? Airbus SE's sales success at the top and bottom ends of the crucial market for single-aisle jets is likely to squeeze Max orders even after the global flying ban is lifted.