In addition, consumers have complained that the surface of the player scratches with normal use. Complaints have been posted on the Cupertino, Calif., computer maker's own support forum and on a Web site called flawedmusicplayer.com, which was set up by an anonymous user.
Apple officials were not immediately available for comment.
On its own support forum, users complained of having scratches on the diminutive player, despite handling the device gingerly.
"I think Apple is going to have a major problem on their hands when enough of these are sold," wrote a customer identified as Richard Spangler. "They chose a poor material for the Nano ... I have treated mine like a king and it already has a few scratches."
On the anonymous site, customers complained of cracking the Nano screen, despite what they considered normal use.
"I had my iPod Nano for exactly four days before the screen cracked on it ... The iPod was placed in my pocket (alone) and into a backpack over the last four days. The unit was not exposed to what I consider harsh treatment," one customer wrote.
People complaining of the device said they were told the damages were not covered by Apple's warranty. That, however, could not be verified with the company.
Apple announced the thinnest version of the iPod music player nearly three weeks ago. The device, which has earned high marks from reviewers, is 0.27 of an inch think, weighs 1.5 ounces and holds as many as 1,000 songs. Pricing starts at $199.
(Editor's note: Please see the follow-up to this story, here.)