I remember hearing an anecdote somewhere, how during one night in the last weeks of his presidency Nixon got so drunk and aggressive, that Henry Kissinger had to call to the Joint Chiefs of Staff that if Nixon orders a nuclear strike that night, confirm first from him if it is for real. Is there any truth to it? In general, how unstable Nixon was during that time? Is there any indication that he was at some point preparing to take other people down with him, perhaps not as literally as with nuclear weapons? And how paralyzed the administration was?
The official was not supposed to be Kissinger, but James Schlesinger. It is suspected the Schlesinger later spread this story. It has not been really confirmed; there is at least one person who says they saw such an order, but no paper trail has ever been established and there are many who think it is apocryphal. I don't know; it's one of my goals to ferret out its origins and reality, as part of an on-going project.
But yes: in the last days of the Nixon Presidency, there were serious questions about his mental state, his drinking, and whether he would relinquish power peacefully. Nixon himself had bragged about being able to kill millions with a phone call (though he did so less in a "look what I can do" mode but more in a "Watergate is such a dumb distraction, if you're talking about trying to limit Presidential power" mode). In the story, Schlesinger supposedly told JCS not to act on any out-there orders from Nixon until they had checked with him first. It is worth noting that had JCS complied with this, they would be technically breaking the law and chain of nuclear command. So it's not clear how meaningful it was or would have been. Nixon in fact would not strictly have to had gone through JCS to use nuclear weapons, either: he could have called up SAC directly, for example. So it's not clear how meaningful it is, and so many have suspected it is just a story Schlesinger liked to tell to make himself seem powerful. Again, I have no idea.
The real fear at the time was not that Nixon would decide to set the world on fire, but that he just wouldn't leave the White House, creating a Constitutional crisis (e.g., who is going to enforce his being ejected? whose side, in practice, would the Secret Service, much less the military, be on?). None of this came to anything, of course, but this was a lingering fear.
For some of the back-and-forth on the Schlesinger story, see here and this (in the latter, search for "I was an Army JAG lawyer" for his account).