“Foxconn is not a sweatshop,” Steve Jobs told the audience at All Things Digital last June, speaking of the world’s largest electronics manufacturer and Apple’s (AAPL) primary supplier of iPhones, iPads, iPods and Macs.

But the company’s 2011 Supplier Responsibility progress report, issued earlier this week, found plenty of room for improvement in its extensive Asian supply chain. In first-time audits of 97 facilities and repeat audits of 30 others the company discovered more than three dozen cases of what it calls “core violations,” including …

• 18 facilities where workers paid such steep hiring fees that they were, in effect, involuntary labor
• 10 facilities where a total of 91 workers under the age of 16 had been hired
• 4 facilities where records were falsified
• 2 instances of “worker endangerment”

Beyond the core violations, there were hints in the body of the report of how hard it is to run an ethical shop in the high-pressure electronics business.

One vocational school involved in hiring underage workers for an Apple supplier had falsified student IDs and threatened to punish students who told the auditors their true ages. Another gathered its workers together and instructed them give auditors false wage payment information — presumably to cover up excessive overtime. At least one supplier offered cash to third-party auditors if they would only sweeten their negative report.

Much of this jibes with the charges laid against Apple by monologist Mike Daisey, who claims in “The Agony and the Ecstasy of Steve Jobs” that he interviewed Foxconn workers as young as 13. Foxconn managers know when the auditors are scheduled to visit, Daisey says, and hide their underage workers out of sight.

But as Daisey is the first to admit, Apple is hardly the only U.S. company that depends on these suppliers, and at least Apple seems to be making a good faith effort to clean up its supply chain’s act, sending underage workers back to school (at the supplier’s expense) and reimbursing a total of $3.4 million to workers who paid what the company considered excessive recruitment fees.

As part of the report, Apple acknowledged for the first time that 137 workers at the Suzhou facility of Wintek, one of Apple’s suppliers, had suffered “adverse health effects” following exposure to n-hexane, a toxic cleaning agent.

A pdf of the full report is available here.

Also on Fortune.com:

• A harsh light on Apple’s supply chain
• Foxconn needs a better trade union
• Foxconn’s 11th: Death by exhaustion

[Follow Philip Elmer-DeWitt on Twitter @philiped]