As I always tell my devices, "The human always wins."
I downloaded the OTA update image twice and it failed at 1% during the install, exactly as others describe.
My phone was stock 5.0.1, never rooted.
Yes, during update I on Wi-Fi, phone placed close to router, phone plugged into charger, microwave oven not on, rabbit's foot next to phone. None of that was the cause of the failure.
I had about 9 GB of free system RAM - should be plenty, right? Not according to some forum posters and according to the installation notes from AT&T. Oh wait. There are never any notes from AT&T. Right.
Read posts on several forums about how to fix it and came up with a couple of things on my own. I was willing to do anything but a factory reset - too much rebuilding since I can't use Titanium Backup. So what did I do? I did them all. And it worked.
And. It. Worked.
.
Here's what I did. Can't tell you which steps were relevant/irrelevant but none of them were a big deal to do/undo. Who cares? If you really must know the answer to this there are some wonderful medications these days to help you with your OCD. Take them.
1. Removed my work email, which needs administrator privileges - my employer requires that I encrypt the device and the SD card
2. I de-encrypted the device (Settings> General tab > Security)
3. I removed a couple of my biggest apps (Waze, Evernote (I keep a lot of notes synced on the device) and a couple of others.
4. My photos and videos are all on the external card so I did not need to remove those - they're all backed up to Google Photos anyway. If yours are in the internal storage, move them to somewhere else.
5. Took the SD card out of the phone.
6. Cleared the cache in Settings> General tab> Storage
7. Cleared the cache individually for Download Manager under Application Manager (the General tab> Storage method does not actually clear all caches, FYI.)
8. Verified that I now had a little over 12 GB of free system RAM out of the total 32 GB.
9. Stopped all background apps using the app switcher.
10. Switched the date/time to manual and set the date to three days from today to trick the update checker.
11. Rebooted the phone in recovery mode so that I could clear the cache partition.
12. Rebooted the phone again from the recovery menu.
13. Burned some sage (Whole Foods), did a couple of Druid incantations (I could only find ones about preventing crop failure - close enough) and I swung the phone around my head exactly 19 times (counter-clockwise, of course.)
The OTA update worked perfectly. Success. 5.1.1 is mine.
1. I put the SD card back in.
2. Put the date/time setting back on automatic.
3. Re-encrypted the device.
4. Restored my work email Exchange account.
5. Reinstalled Waze, Evernote, and the couple of other apps that I had removed.
Was all of that necessary? Probably not. Very likely not. But the update worked, I have 5.1.1 and now my house smells delicious from the sage.
As I periodically remind all of the various machines in my house, "The human always wins." They know this, they understand this, and they know about the e-recycling bin that awaits them otherwise.
The UI is MUCH more responsive - far snappier than one would expect from clearing out memory and rebuilding database indexes alone). App switching is quick. So far (so far) I'm not getting those annoying-as-sh1t delayed home screen refreshes on the Google Now launcher.
Battery life seems to be unaffected. I use only Qualcomm Quick Charge 2.0 compliant chargers (including my car charger) and I carry two hot spare batteries and an external charger when I'm on the road. The Note 6 better have a swappable battery or I'll be a former Samsung customer.