My problem fixed itself. I logged back onto the developer page today and noticed that the Request Log had updated. My Raspberry Pi code was not running, but now I can see yesterday's requests in the log.
Since I had the same problem on my Raspberry Pi and on my iPhone (failure of the Request Log to show anything but "Waiting for requests" and a failure of the graphs to update/scroll without me hitting F5 over and over), I don't think it was the Pi or the phone at fault.
I suggest the following three possibilities: 1: Perhaps it can take a day or so for a new Xively account to start working? All of my problems were on Day 1 of my new Xively account. 2: Perhaps there was a general problem with the system yesterday. Maybe only with newly formed channels or accounts. 3: Maybe someone behind the scenes saw my post and fixed my account.
Anyway, everything seems to be working fine now on the Pi. Time to get to work on a "real" project!