And no, if you're thinking I'm writing to a formula field, that's not it - read on....
I've been seeing this error sporadically during an upsert on one, and only one, org.
Upsert failed. First exception on row 0 with id a1H00000000VR5lEAG; first error: UNKNOWN_EXCEPTION, Cannot set the value of a calculated field: 
I've done a search for "Cannot set the value of a calculated field" (in quotes) and, believe it or not, it comes up with just one unrelated response.
And no, it's not the obvious - I'm not setting the ID, and if you try to update a formula field, you get the error "Field is not writable" which, as you would expect, returns gazillions of hits when searched.
In terms of being sporadic - it might appear once every week or two. So we're talking maybe one error in >100K upserts on this object. On this one org - nowhere else.
Notice that it doesn't actually say what field is impacted. And, to add to the confusion - this is an upsert of a custom object in a managed package. There are no triggers or workflows on the object.
I'm very much at a loss - without the ability to reproduce it, contacting SFDC support is likely to be a waste of time. So, if anyone has seen this before and has any suggestions or context to provide, I'd greatly appreciate it.