First off, keeping a "things to do today" list is OK. I think a LOT of us do that. In fact, I just heard David Allen in a Connect webinar say he does this, too, so, if the man himself says go for it, why not.
Tickler files, if you use them regularly and consistently, are a GREAT place for reminders like the mouthguard. I look at my next day's folder the night before and create a list for the day based on those notes. If I see "call dentist re: mouthguard" then I know it has to happen the next day.
As an aside, our daughter does martial arts and has braces. Her dentist did a mold of her mouth with braces and had a custom guard made. It was a disaster. (Actually, the whole practice was a disaster and she ended up having them removed and put on by an orthodontist instead of her dentist who "did braces" - ugh. Poor kid.) So if your son has braces, don't get the molded ones because their teeth MOVE in braces! Her orthodontist gave her a very basic one that she loves... I can find out the brand if you or anyone else is interested.So, to your point about how GTD is supposed to work: built into the GTD system are ways to handle the three kinds of work you have...
Defining your work (processing a note from your son's coach saying he needs a mouthguard into your tickler or next action errands list)
Pre-defined work (you see that "get a mouthguard" is on your errands list and you run the errand or plan when you're going to run it)
Work As It Appears (your son says he needs a mouthguard a.s.a.p.)
That third one is where your urgent item fell into the system. That said, really, really urgent things like a snake bite or a car crash handle themselves, don't they? I mean, you just handle them, and everything else waits, right?!
Hope all that rambling helps a little!
constant forward pressure