This one looks like a deal breaker. According to the PS Vita FAQ over at Sony’s Japanese website, the handheld may not support “Game Archives” which appears to be the term used for PsOne Classics available on the PSN over there.
Is this a way for Sony to re releasing games like Final Fantasy VII or the Chrono series? The FAQ is being cautious with this information, so things may change in the future as more details get released and we get closer to the launch date of the system. This could just be a case of miscommunication, you never know.