This is similar to what I have seen, which is that errors show up in no apparent relationship to rules actually being triggered.
EDIT #1: I came home today and saw an endless stream of errors in my log from while I had been gone at work; they were all attributed to a single rule. I went into that rule's details page, hit "Update", then hit "Done", and the errors have stopped. I'm now going through all my rules and hitting "Update" and "Done" to see if this overwrites (and corrects) any underlying database errors.
EDIT #2: Turns out the above corrected only that error, not the others. I have done another soft reset + restore, but Iām still getting generally the same errors for which I started this thread. Not sure if any additional troubleshooting steps are available after multiple soft resets + restores have not eliminated the errors, but if anyone has any suggestions, Iām all ears...