As IGN reports, Sony's issued a statement on their official Japanese site regarding the issues some Vita early adopters in Japan are experiencing. These include the device randomly turning off, the system freezing, being unable to connect to data services, and PSN accounts not registering. The video above shows some examples.
The problems are apparently ubiquitous enough that Sony felt the need to respond: "Recently, we have received many inquiries via the PlayStation Vita Information Center as well as through normal channels. Depending on time, it may continue to be difficult to contact us over the phone. We're sorry to have caused such an inconvenience. As for inquiries regarding the PlayStation Vita, we have tried to make its operation as easy as possible. We've prepared a Q&A below, so before you contact us please consult it."
The Q&A addresses several of the issues we've mentioned. IGN goes on to report that response from consumers seemed lukewarm upon the Vita's launch, though CBS disagrees ("PS Vita off to strong start").