For years, Boeing Co. and the Federal Aviation Administration handled 787 Dreamliner deliveries as though the perfect was the enemy of the good.

The FAA allowed the plane maker to deliver the wide-body jets with some minor flaws, so long as there was no immediate threat to safety. The expectation was that Boeing would fix such defects after the planes began carrying passengers, according to government officials and current and former Boeing executives.

That approach doesn’t fly anymore. Two deadly crashes of a different Boeing airplane, the 737 MAX, ushered in a new era of intense scrutiny of everything rolling out of Boeing’s factories.

The result has been a string of Dreamliner delays that have become headaches for both Boeing and the airlines waiting for delivery of scores of 787s worth more than $25 billion. Production snafus have popped up one after the other. Some of the latest involve titanium parts, glue and fasteners, people familiar with the matter said.

On Wednesday morning, Boeing said it had submitted a plan to the FAA for resolving production problems, a key step in restarting Dreamliner deliveries. Those could resume this summer if regulators approve the proposal, people familiar with the matter said.

The FAA will no longer haggle over whether Boeing can deliver 787s that diverge from agency-approved designs and federal regulations. “Before, we’d work it out,” said one government official familiar with the FAA’s Dreamliner work. Now, this official said, “We’re not negotiating.”

Amid the scrutiny, Boeing employees found defects on their own and began taking a harder look at how the company produced Dreamliners. They found more problems.

In 2019, they detected gaps between sections of the Dreamliner’s fuselage that were slightly wider than specified in the FAA-approved designs. The gaps, about the width of a piece of paper, were wider than the manufacturing tolerance of 0.005 of an inch allowed under the approved design.

“What happens when you take a microscope to anything?” said John Plueger, chief executive of Air Lease Corp.

, a major buyer of Boeing aircraft that it leases to airlines. “You find more stuff.”

What previously might have been deemed minor issues are now garnering significant attention. “There is some risk of the pendulum swinging too far the other way,” Mr. Plueger said.

It isn’t that Boeing suddenly stopped making Dreamliners properly. It found previously unknown production problems that in many cases had introduced minor defects in planes already flying. Those led to more discoveries, which fueled more questions from regulators.

The halt to deliveries has frustrated some of Boeing’s most important customers, including American Airlines Group Inc. and United Airlines Holdings Inc. The twin-aisle jets, whose models can carry between about 250 and 340 passengers, are popular with airlines, which often use them on long-haul international routes that wouldn’t otherwise be profitable with larger aircraft. The Dreamliner made its debut in 2011 and has had an excellent safety record.

Boeing CEO David Calhoun touring the company’s 787 Dreamliner factory in South Carolina in January.

Photo: Boeing

The plane maker is counting on eventual Dreamliner deliveries this year to catch up with demand and generate cash to help it pay down its debt. Now that Boeing has submitted its paperwork to the FAA, it hopes to get a green light to resume deliveries within seven to 11 weeks, people familiar with the matter said. The FAA said Wednesday that safety drives the pace of the agency’s reviews.

During a call with analysts on Wednesday, Chief Executive David Calhoun declined to speculate about when the FAA might approve Dreamliner deliveries, but expressed confidence in the quality of Boeing’s submission to regulators. “It’s been a long, hard run, but I feel really good about where we are,” he said.

Mr. Calhoun has said he is giving Boeing engineers time to fix the Dreamliner’s problems and retool its production system. He has said Boeing would follow the same playbook as it did with the 737 MAX, which regulators grounded for nearly two years to fix problems related to software, hardware and training.

“We have to have exactly the same objective with the ’87,” Mr. Calhoun said at a meeting with executives in October. “If we get there—and we will—it will pay for itself.”

A Boeing spokesman said the company was completing thorough inspections of the 787 production line and supply chain to ensure they conform to Boeing’s specifications. The company declined to make Mr. Calhoun available for comment.

In February, the FAA further tightened its oversight of the Dreamliner. It said its inspectors would check each jet individually, rather than let the plane maker perform routine final safety signoffs, as the FAA had permitted it to do for years.

Then-FAA Administrator Steve Dickson testified in November at a Senate committee hearing on aviation safety.

Photo: Rod Lamkey/CNP/Zuma Press

That same month, then-FAA Administrator Steve Dickson, who stepped down on March 31, said about Boeing: “They’ve got to produce the quality on their production line that we’re looking for and that they’ve committed to.”

In the years leading up to the 737 MAX crashes in 2018 and 2019, Boeing enjoyed more sway over regulatory matters. The FAA delegated an increasing number of tasks to a group of Boeing employees authorized to work on the agency’s behalf.

The 737 MAX accidents, which claimed 346 lives, exposed problems with the FAA’s oversight of Boeing. A U.S. House committee’s investigation documented cases in which senior FAA managers overruled the agency’s front-line experts in favor of Boeing, on safety matters related to lightning protection and rudder cables. The FAA has said its managers were also aviation experts.

Congress overhauled how regulators certify new aircraft designs and oversee employees of manufacturers working on the agency’s behalf. The agency now has more power to choose which Boeing employees represent the FAA’s interests, and there are new protections for them from undue pressure by company managers.

The wreckage of a Boeing 737 MAX that crashed near Bishoftu, Ethiopia, in 2019.

Photo: Mulugeta Ayene/Associated Press

“The good old days got us to where we are today,” said U.S. Rep. Rick Larsen (D., Wash.), who represents much of Boeing’s workforce in the Seattle area and is chairman of the House Transportation Committee’s aviation subcommittee. “We have a certification reform bill because of the good old days, which were pretty bad for 346 people and family.”

The problems Boeing employees found initially were minor by themselves: improper-size shims in the minute gaps they had found between sections of the fuselage, and areas where the fuselage skin wasn’t sufficiently smooth.

But the imperfections could add up to a more serious problem with the plane’s structural integrity, according to industry and government officials. Undetected flaws can result in premature aging that airlines don’t know to check for and repair, the officials said.

After finding the Dreamliner defects, Boeing has run stress tests to determine whether the structure of any 787s with such defects in airlines’ fleets could easily withstand extreme flying conditions. In August 2020, Boeing teams identified eight in-service Dreamliners that didn’t meet “limit load requirements,” and recommended airlines ground them for immediate fixes.

Nearly all of the rest of Boeing’s analyses since then have found Dreamliners have more than enough built-in protection despite the imperfections. The flaws can be inspected and fixed, if needed, during routine maintenance.

Workers at Boeing’s Dreamliner facility in North Charleston, S.C.

Photo: Travis Dove/Bloomberg News

As Boeing’s factory churned out more planes, Boeing employees kept looking for additional flaws. The company halted Dreamliner deliveries in October 2020 after it found more flaws and widened inspections. The process was initiated by Boeing, which reported the findings to the FAA, according to people familiar with the matter.

Boeing also pushed its global network of suppliers to examine the 787 parts they produce. Suppliers found more problems. They alerted Boeing of “notices of escape,” factory jargon for defects. That meant more parts to fix, such as titanium pieces that were weaker than they should be. And it meant more planes to examine, both undelivered new jets and ones in service for years.

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Delays snowballed. Company projections for when it could deliver Dreamliners came and went. Customers grew frustrated.

American Airlines said it would reduce its summer 2022 flying schedule because its new Dreamliners wouldn’t arrive in time. “We don’t have as many airplanes as we want,” then-CEO Doug Parker said at an industry conference March 15. “We’re not happy about that.” Mr. Parker, who remains chairman, retired as CEO on March 31.

Boeing lost 47 firm orders for Dreamliners last year, leaving it with 411 deliveries to fulfill at the end of 2021, according to a securities filing.

Mr. Plueger, the Air Lease CEO, said he has repeatedly conveyed a message to senior Boeing executives in the Seattle area, where its commercial jetliner arm is based. “You just have to be a reliable partner and you have to get through this,” he recalled telling them.

Boeing has said it would book $5.5 billion in costs related to the Dreamliner problems.

After the 737 MAX crashes, Boeing reorganized its engineering department. Part of the aim was to reduce the influence of cost and schedule on design and safety matters.

An Air Canada Dreamliner in service last year at the Montreal airport.

Photo: Christinne Muschi/Bloomberg News

Federal lawmakers strengthened protections for employees in Boeing’s Organization Designation Authorization, or ODA, unit, who are empowered to work on the FAA’s behalf. The agency now wants to use Boeing’s ODA unit as an additional layer of scrutiny: in-house experts who are more familiar than the FAA’s staff with the Dreamliner.

It was an ODA member who flagged a quality-control problem with the Dreamliner cockpit windows, according to people familiar with the matter. Boeing drew up new specifications for the window supplier, PPG Industries Inc., a Pittsburgh company, the people said. The retooling resulted in delays for new windows. Boeing at one point was running so low on windows that it harvested spares from undelivered Dreamliners for jets already in service, they said.

The Boeing spokesman said the company was working to ensure cockpit windows meet all specifications. PPG declined to comment.

Mr. Calhoun, at the October meeting with executives, said Boeing needs to continue improving its manufacturing culture. “Our quality people don’t feel like they’re being listened to,” Mr. Calhoun said. “That has to change.”

Senior FAA officials have been broadly pleased with Boeing’s improvements but not with their pace, according to people familiar with the matter. Agency officials have at times complained to the plane maker’s executives that lower-level Boeing employees who work with the FAA haven’t seemed to be getting the message, those people said. In February, Mr. Dickson said Boeing overall had “really improved the discipline within their engineering organization.”

If Boeing manages to resume Dreamliner deliveries this summer, the freeze will have lasted about as long as the grounding of its 737 MAX.

—Micah Maidenberg contributed to this article.

Write to Andrew Tangel at Andrew.Tangel@wsj.com