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.
I'm not really an expert, but when someone generates a chain of transactions in rapid sequence it looks like something like this can happen. The simple lesson is try to avoid such sequences by not sending bitcoins through multiple TX's if you have anything to say about it.
I've never run into such a situation myself, at least not that I've noticed. Normally a person is going to be spending bitcoin that they've had for days/weeks/months, not a few minutes or hours, so the funds they send will already be confirmed. And most 3rd party services and software wallets require a certain level of confirmations before they would let you send funds anyway. In fact, it makes me curious as to how the sender of your bitcoin managed to (apparently) circumvent that and spend unconfirmed bitcoin! Did you buy the bitcoin on an online exchange like Coinbase, or from some guy on a street with Localbitcoins, or what? (Just curious, don't answer if you don't want to.)