Hey, I've had the infamous "Invalid Code Error 01" on my PodXT, see http://line6.com/supportarchivenew/thread/58952
I finally managed to take the time to fix it (yeah, I know, years later). The problem kept getting worse and worse. Finally I tracked it down to improperly soldered components on the PCB: by applying pressure to a very specific spot on the PCB before turning the Pod on, I was able to make it work for some time.
In the end, I've had to reflow the Analog Device DSP to fix the problem. I used a hot air soldering rework station and some flux, but there are other reflow methods (check google, it's especially popular with some well known gaming console ;).
So, I blame it on poor manufacturing process, but at least it's fixable if you have the time, the tools and the know-how.
HTH