Now that you know what the culprit is, this might be an easy fix. Where the cord goes into the disposal, there may be a cover plate that you can remove and check the connection. If the cord is made with stranded conductors, it's possible a strand was missed when installed on the terminals and finally found its way to the metal case. It'd just take a few minutes to check the connections to see if it's something obvious and easy to fix.
And yeah, I'm pretty sure the code changed a few years ago that dishawashers and all under cabinet stuff has to be on a GFCI now...that's easy to change out too--usually...but not in my case, normally.
