• The probe was initiated after a door panel blew off a 737 Max 9 during an Alaska Airlines flight in early January and comes amid intense scrutiny of the company's practices
• FAA auditors found that out of 89 product audits that were conducted, Boeing passed 56 tests and failed 33 of them, according to the NYT report.

U.S. air safety regulators found "dozens of problems" at facilities owned by Boeing and one of its key suppliers after a six-week audit of the production of the 737 Max jet, according to The New York Times. 

The Federal Aviation Administration started the probe after a door panel blew off a 737 Max 9 flight on Alaska Airlines in early January, an incident that has attracted intense scrutiny of Boeing's quality-control practices. 

The NYT report, published Tuesday, was based on a review of an internal FAA slide presentation and offered a glimpse into the numerous issues found by auditors. Many of the problems fell under the category of failure to follow "approved manufacturing processes" and failure to keep proper quality control documentation, according to the Times.

FAA auditors found that out of 89 product audits that were conducted, Boeing passed 56 tests and failed 33 of them, according to the report.

During the six-week audit, the FAA also conducted 13 product audits that focused on Spirit AeroSystems, which makes fuselages for the Boeing 737 Max — of those, only six audits resulting in passing grades, and seven failed, the NYT said.

A document reviewed by the Times found that a mechanic at Spirit used a hotel key card to check a door seal. In another instance, the FAA reportedly saw Spirit mechanics apply liquid Dawn soap to a door seal to use as a lubricant in the "fit-up process." 

A spokesman for Spirit reportedly said the company was "reviewing all identified nonconformities for corrective action."

In late February, the FAA gave Boeing 90 days to develop a plan for quality-control improvements. Around the same time, an expert panel's report on Boeing found a "disconnect" between its senior management and employees regarding safety culture. 

The panel report had been required by the U.S. Congress after two crashes in 2018 and 2019 involving Boeing 737 Max planes killed all the passengers and crew aboard — a total of 346 people.

In response to the NYT report and recent expert panel report, Boeing said it continues "to implement immediate changes and develop a comprehensive action plan to strengthen safety and quality." 

"We are squarely focused on taking significant, demonstrated action with transparency at every turn," Boeing said in a statement to CNBC. 

In addition to the FAA, the National Transportation Safety Board is looking into what caused the 737 Max jet door panel to blow off during the Alaska Airlines incident, and the Justice Department has reportedly begun a criminal investigation into the company. 

— CNBC's Phil LeBeau contributed to this report.

Read the full report from The New York Times.