Your experience with the DR-680 is interesting. I used one for a few years, myself. I actually did 15 features on that little sucker, and an untold number of commercials, TV spots, etc. For a $500 mixer, it's a trooper. It works well for what it is. It just can't be expected to be anything it's not.
I did once miss a take on it, when it refused to roll, due to overheating (on a ridiculously hot set, on an August day). Other than that, no issues.
Sorry to hear you had trouble with yours. Power supply issues can cripple any device, obviously. I found the 680 worked very, very well with a 10Ah Tracer LiPO battery. I used to get nearly 2 days out of that thing, with never a hiccup.
Speaking of power, the HS-P82 is an energy hog, just so you know. For that, I use a pair of 32Ah Poweradd Pilot Pros. I get about 8 hours out of each, running at 12V. I swap them each day at lunch, and have never had any issues. (The Tracer that could go 2 days powering the DR-680 lasts about 4-5 hours on the HS-P82, by the way.)
As for backups, I'm sure you'll love the HS-P82's dual card system. There are always 2 copies of everything (and I also usually run 2 camera hops, so that's 4 copies).
Further, you don't lose the current take if you do lose power, which is a really nice feature. It writes and saves the raw audio data in real time. Worst case, you might just need to do a little bit of file header repair, if the file doesn't have time to get finalized, but the audio will always be there, either way. That's actually saved my life twice now, on shoots when I forgot to swap batteries, due to not having had a proper lunch break.
I do agree with you, by the way, that realtime spec analysis is a great thing. I used to do that, back when I was strictly a cart-based mixer. The laptop was always there for spec and wave display. These days, I'm nearly always one-manning it, though, so I couldn't pay attention to a spectrogram, even if I wanted to.
That said, I've found the Spectroid app on my tablet to be super useful for getting a general idea of the soundscape. It's not as accurate as a computer-based system, of course, but it's good enough to be able to judge whether or not ambient noise will be subtractable without noticeably affecting dialog. It's great to be able to walk up and SHOW the AD what's going on, rather than just tell.
"Hey, you see those lines right there? Those are the hum of that refrigerator in the next room. See these wavy blobs that appear when I talk? That's where the dialog will be. See how the wavy blobs and the lines are in the same range on the graph? That means the fridge needs to be unplugged. Please tell G&E to do that. Now, you see these dots over here, way above the wavy blobs? Those are the beeps from that answering machine the PA's have been trying to figure out how to disable for the past half hour. Those dots can taken out in 2 clicks, so quit stressing over the damned beeps, and let's roll."
It may sound silly when typed out like that, but I've actually had that exact conversation.