In Activity Monitor, are two processes that are highlighted in red text:
1) software updated (Not Responding)
2) com.apple.geod (Not Responding) [This appears with a plugin icon.]

I don't know what to do, if anything, with these anomalous conditions. Should I be concerned?

Google turns up several discussions about com.apple.geod including several suggested fixes, but other than the information that this is related to location services and apparently crashes if there is any network interruption. I think this is a "report it to Apple and let them worry about it" item. There is also a lot of evidence the "fixes" either do not work or do not last.

I just force-quit non-responsive processes out of hand and go about my business; recurring instances may present a problem.

com.apple.geod is apparently a widespread issue in Yosemite.

You can check to see what's going on in Activity Monitor by highlighting the offending item and selecting Inspect.
Or you can simply jettison the offending item by selecting Quit Process.
Then see what happens.

Have you ever been able to make heads or tails out of the details presented by "Inspect"?

They just make me roll my eyes.

Yeah, it's a tad bewildering and stultifying.
But there might be some news he can use.

I tried the Inspect routine, and as you surmised, no meaningful data, well, at least to moi. I was hoping for clue, such as an app name or the like. Alas, no joy.

So after verifying my backups, and as the miscreants were not responding (anyway), I force quit them.

I suppose I'll know in a few days what chaos ensues.