Apparently, from what I read, deteriorating powder does become unstable and is likely to do anything, including explode.
However, as
Mouser&9 explained, powder that is going bad often leaks at the primers and bullets. If a cartridge or can is opened, it will have a very distinct acid smell as the nitric acid leaches out of the nitrocellulose. It will often display a reddish bloom that works though the powder and keeps it from pouring like we're accustomed to seeing.
You are correct, the primers are corrosive. My son had one of those Mousers and the bore and head spacing was shot. If your bore is already showing signs of demise, then (after a thorough external exam) you might shoot some of the ammo and see.
A few stolen photos for my pals....
This may be the only indication you see...Here's some US-made 30-06 from 1989 already gone bad...