When mechanical problems occur, pilots rely on what's known as the Quick Reference Handbook -- an electronic checklist for troubleshooting.

"One guy flies while the other guy fixes, and then you make a decision," says Justin Schlechter, a 13-year airline pilot.

Schlechter remembers a problem aboard his aircraft in 2004 when a passenger looking out a window spotted a minor fuel leak near the wing. After referring to the checklist, Schlechter diverted the airliner and landed in nearby Richmond, Va., as a precaution.

Another time, a crack appeared in Schlechter's cockpit windshield. "It was a complete nonevent," he says. The flight continued to its scheduled destination.

"Windshields crack all the time," says Goglia. Measuring inches thick and multilayered, airliner windshields are designed to take a beating from weather and the occasional bird.

The cracked engines reported on Dreamliners in 2012 were likely isolated incidents, Ordonez says. As for random window cracks and fuel and oil leaks, Boeing can solve these kinds of problems without much difficulty, he says.

Worldwide, Dreamliners fly 150 flights daily, Boeing said last week. In a statement released Wednesday, Boeing reacted to the FAA grounding.

"We are confident the 787 is safe and we stand behind its overall integrity. We will be taking every necessary step in the coming days to assure our customers and the traveling public of the 787's safety and to return the airplanes to service," said Boeing Chairman, President and CEO Jim McNerney.

"I still would get on the airplane," Hiatt says. It may be the most watched airliner in the world now. "That airplane is being looked at so closely both before and after every flight that it borders on the ridiculous."

"Now, I guess people should be a little concerned," says Ordonez. But bottom line, he says, "I'd fly it."