The general consensus in UK press reports seems to be that Samsung dealt with things well initially, but were like rabbits caught in headlights second time around. One can only imagine the panic & buck passing going on at Samsung HQ as they realised that the replacement devices had a problem. Even last night, Samsung UK were apparently still telling UK customers & the tech press that Note 7s were safe to use (though refusing to allow BBC to buy one), yet by this morning clearly a high level decision had been taken to recall, then later to announce that production was halted, and then later still that the Note 7 was being discontinued. That slow drip of news seems to be a bit of a PR blunder as it meant that the story kept growing even today and kept the story in the headlines - a single press release would have got all the pain out in one go.
For me, the odd thing is a report where Samsung apparently claimed that the replacement devices had a different problem. If that's the case, then this seems to disprove their own story that a faulty battery batch was to blame (since if that were the case, the replacements should not have had any problem). What seems possible is that there were faulty batteries in the first batch, but that this was not the root cause of the problem either before or after the first recall. Given the decision to discontinue, its more likely that an inherent design defect was to blame.
As others have said, no doubt Apple and others will be watching closely (and testing a few devices in a lab somewhere) to learn from the problem, just as in other industries - for example Boeing and Airbus take keen interests in each other's problems to ensure their designs don't have the same problem when air accident investigation reports are released. It might be a problem that Samsung inflicted on themselves, or might be that they pushed smartphone design too far and industry best practice/knowledge will need updating. Their PR department will be similarly reviewing events to see what they can learn from Samsung's management of the story.
It'll be interesting to see how Schiller, Cook et al respond when questions about the Note 7 inevitably get asked in future interviews etc. I doubt they'll crow about it, whatever the cause was, but their tone may give a clue as to whether they think it was a self-inflicted design mistake or something that they need to learn from themselves in future models.