Last week, retired marketing specialist Nora Probasco called her brother with a half-serious, half-joking question: Was she adopted?

The issue came up after the 59-year-old genealogy hobbyist from Louisville, Ky., received the results of a test she took through 23andMe, a Google-backed firm that allows people to learn more about their ancestry and some medical conditions through DNA analysis.

"I was shocked," she said. "What it came down to, the way I know to read them, is that my mom is not my mom."

To her relief, it turned out to be a mistake. Last Friday, the Mountain View firm acknowledged in a post on its Web site that it mixed up the samples of 96 clients and sent them the wrong ones. The company corrected the mistake relatively quickly, but observers see the potential for similar errors that could lead individuals to make ill-informed decisions regarding their health.

The company, which was founded in 2006, said in an e-mail that the mistake occurred when a tray with 96 samples was misplaced. The company added that new procedures have been...