This time, however, the update produced a slew of error messages. For what appeared to be each repository it checked, it printed an error message saying
Skipping acquire of configured file <something with "i686" in it> as repository <whatever> doesn't support architecture 'i686'After all the architecture error messages, I also got one about a problem with a GPG encryption key on a CRAN mirror. That message had been popping up, harmlessly, on each update for quite a while, so I did not worry about it.
The PC is a 64-bit machine, with an AMD processor, and I'm used to architecture references that contain either "amd64" or "x86_64" rather than "i686". So my suspicious was that something had messed up a setting somewhere on the machine that identified the architecture to the updater. Running uname -m in a terminal got me "x86_64", confirming that the machine itself was not undergoing any sort of identity crisis.
After a fruitless search for a malformed configuration file, I went to a Mint help forum, where I received a few answers. One said it was a server error, and I should just wait for them to fix it. That didn't hold water for a couple of reasons. First, it would require simultaneous problems on a whole bunch of unrelated repository servers, which would be a bit too coincidental. Second, my laptop (also using an AMD 64-bit chip, but running Mint 18.0 Sarah and a slightly older version of the updater) had no problem updating. Another suggestion, reinstalling the updater, also bore no fruit.
Along the way, I discovered that in fact two repositories were being updated correctly. Those two, not coincidentally, specified "[arch=amd64]" in their source listings. Adding that string to all the other PPAs and extra repositories worked, albeit at some cost (the updater started to label the repositories as "arch=amd64" rather than by their correct names). Unfortunately, the updater would not let me use that trick on the two main repositories (one for Mint, one for Ubuntu), which left me still looking for a fix.
Someone on the help forum suggested disabling all the PPAs on my list of sources and trying again. I did that, and (crucially) also disabled sources in the "Additional repositories" list, leaving just the Mint and Ubuntu repositories. Lo and behold, the update went through. So I started restoring the other repositories in a binary search, and found the culprit. Remember the CRAN mirror that had a problem with its encryption key? If I disabled just that source, which was in the "Additional repositories" list, things worked. So I switched mirrors, reloaded the public key, and things are back to normal.
I have no idea why the encryption key error, which I'd been getting for weeks if not months, suddenly caused things to go splat across the board -- and even less intuition as to why a bad encryption key would cause the updater to start using the wrong architecture code. For now, though, I'll settle for having updates working again.
Update 06/28/17: It happened again, this time with the Revolution Analytics CRAN mirror yielding the message "server certificate verification failed" and something about a missing file (which I assume was their certificate). So I switched to yet another mirror, and we're back in business ... for the moment. I don't like the idea of downloading software over insecure/unencrypted connections (for reasons that I would hope are obvious), but this is getting tedious. Note to server admins: please keep on top of your certificate deployment.
Update 07/25/17: Here we go again, only this time with a new wrinkle. I added a PPA, did an update to the package list, and got the 'i686' architecture message for every repository. This time, though, there were no certificate errors, and disabling every source I could (including the newly added PPA) did not help. So something else was at fault. After searching the web for help, I tried the following commands in a terminal:
The first one listed 'amd64' (which is correct); the second listed 'i386' and 'i686'. I have one or more packages installed that actually do require the 'i386' architecture -- packages that only exist in 32 bit form (don't ask me which, I've forgotten) -- but none that I know of requiring 'i686'. So, again in a terminal, I ran
sudo dpkg --remove-architecture i686
and (after restoring all my repos) was able to update successfully. I don't know if adding the new PPA caused the 'i686' architecture to return, zombie-like, for another go around, or whether the package manager just wants to reset to that whenever I'm not looking. In any event, I think I have a fix now, but we'll see if it's permanent or temporary.