Thanks for the advice here.
My iPhone 5 informed me this morning that it hadn't been backed up to iCloud for 3 weeks, even though that's how my settings were configured. On my phone, I went to Settings > iCloud > Storage & Backup and clicked the "Back Up Now" at the bottom. It worked on the second try and now my phone and iTunes say that my phone is now backed up in iCloud. No Terms and Conditions for me, either. I'll have to keep an eye on iCloud to see if it now starts taking automated daily backups again.
I'm expecting iOS 7 updates when the new iPads show up, so hopefully this and other minor issues will be corrected.