We've contacted Sony to find out what's causing the issue, and when we can expect to get back to chasing down the Origami Killer. He might just be able to make a clean getaway while we suffer through this downtime.
Update: Sony has acknowledged the issue, and is "looking into it." We've yet to hear an official word on what the problem is, though it seems to be a bit larger than just the PSN. Owners of PS3 Phats are reporting that the date on their console has reverted to 12/31/1999, which is likely the cause of the data-corrupting errors. Some Phat-owners have reported receiving the errors while their console was offline, which is upsetting, to say the least. We'll let you know when we hear official word from Sony.
Update 2: It's been 11 hours since our last update from Sony, and Phat PS3s worldwide are still unable to play Trophy-supported games. The issue is almost certainly non-PSN related, and appears to be a firmware issue caused by the screwy time and date settings. The issue is also affecting debug consoles, which Develop reports is preventing PS3 game developers from working on their projects. We'll keep pushing Sony on this issue. Happy New Year, everyone!
Update 3: Sony has responded to the internal clock error, and is advising PS3 Phat owners to leave them turned off until the issue can be fixed -- hopefully within the next 24 hours. Read here for more info.
Update 4: The issue has been resolved.