A six-week audit by the Federal Aviation Administration of Boeing’s production of the 737 Max jet found dozens of problems throughout the manufacturing process at the plane maker and one of its key suppliers, according to a slide presentation reviewed by The New York Times.

The air-safety regulator initiated the examination after a door panel blew off a 737 Max 9 during an Alaska Airlines flight in early January. Last week, the agency announced that the audit had found “multiple instances” in which Boeing and the supplier, Spirit AeroSystems, failed to comply with quality-control requirements, though it did not provide specifics about the findings.

The presentation reviewed by The Times, though highly technical, offers a more detailed picture of what the audit turned up. Since the Alaska Airlines episode, Boeing has come under intense scrutiny over its quality-control practices, and the findings add to the body of evidence about manufacturing lapses at the company.

For the portion of the examination focused on Boeing, the F.A.A. conducted 89 product audits, a type of review that looks at aspects of the production process. The plane maker passed 56 of the audits and failed 33 of them, with a total of 97 instances of alleged noncompliance, according to the presentation.

The F.A.A. also conducted 13 product audits for the part of the inquiry that focused on Spirit AeroSystems, which makes the fuselage, or body, of the 737 Max. Six of those audits resulted in passing grades, and seven resulted in failing ones, the presentation said.

At one point during the examination, the air-safety agency observed mechanics at Spirit using a hotel key card to check a door seal, according to a document that describes some of the findings. That action was “not identified/documented/called-out in the production order,” the document said.

In another instance, the F.A.A. saw Spirit mechanics apply liquid Dawn soap to a door seal “as lubricant in the fit-up process,” according to the document. The door seal was then cleaned with a wet cheesecloth, the document said, noting that instructions were “vague and unclear on what specifications/actions are to be followed or recorded by the mechanic.”

Asked about the appropriateness of using a hotel key card or Dawn soap in those situations, a spokesman for Spirit, Joe Buccino, said the company was “reviewing all identified nonconformities for corrective action.”

Boeing did not immediately comment on the results of the audit. In late February, the F.A.A. gave the company 90 days to develop a plan for quality-control improvements. In response, its chief executive, Dave Calhoun, said that “we have a clear picture of what needs to be done,” citing in part the audit findings.

Boeing said this month that it was in talks to acquire Spirit, which it spun out in 2005. Mr. Buccino said on Monday that Spirit had received preliminary audit findings from the F.A.A. and planned to work with Boeing to address what the regulator had raised. He said Spirit’s goal was to reduce to zero the number of defects and errors in its processes.

“Meanwhile, we continue multiple efforts undertaken to improve our safety and quality programs,” Mr. Buccino said. “These improvements focus on human factors and other steps to minimize nonconformities.”

The F.A.A. said it could not release specifics about the audit because of its ongoing investigation into Boeing in response to the Alaska Airlines episode. In addition to that inquiry, the National Transportation Safety Board is investigating what caused the door panel to blow off the plane, and the Justice Department has begun a criminal investigation.

During the F.A.A.’s examination, the agency deployed as many as 20 auditors at Boeing and roughly half a dozen at Spirit, according to the slide presentation. Boeing assembles the 737 Max at its plant in Renton, Wash., while Spirit builds the plane’s fuselage at its factory in Wichita, Kan.

The audit at Boeing was wide ranging, covering many parts of the 737 Max, including its wings and an assortment of other systems.

Many of the problems found by auditors fell in the category of not following an “approved manufacturing process, procedure or instruction,” according to the presentation. Some other issues dealt with quality-control documentation.

One audit dealt with the component that blew off the Alaska Airlines jet, known as a door plug. Boeing failed that check, according to the presentation. Some of the issues flagged by that audit related to inspection and quality-control documentation, though the exact findings were not detailed in the presentation.

The F.A.A.’s examination also explored how well Boeing’s employees understood the company’s quality-control processes. The agency interviewed six company engineers and scored their responses, and the overall average score came out to only 58 percent.

One audit at Spirit that focused on the door plug component found five problems. One of those problems, the presentation said, was that Boeing “failed to provide evidence of approval of minor design change under a method acceptable to the F.A.A.” It was not clear from the presentation what the design change was.

Another audit dealt with the installation of the door plug, and it was among those that Spirit failed. The audit raised concerns about the Spirit technicians who carried out the work and found that the company “failed to determine the knowledge necessary for the operation of its processes.”

Other audits that Spirit failed included one that involved a cargo door and another that dealt with the installation of cockpit windows.