Thanks for the reassuring responses
I don't pretend to quite understand what has happened here, but it's good to know that it's apparently a recognized issue.
Could someone offer a brief, noob-friendly outline as to why a84fbe6372584f39363e01902e96e4e67858c6c9e8a6cfe511c0a7df8f198420 (not my wallet) is unconfirmed and how I can avoid this happening again? Not terribly comfortable with the notion that I can spend bitcoins and have them confirmed in minutes not hours, but only conditionally, depending on the way in which they were sent to me.