"Fail-Safe", from 1964, came out about the same time as "Dr. Strangelove." They were essentially the same story - US planes erroneously sent to bomb Russia, and the attempt to have them recalled. "Fail-Safe" was a straight suspense-drama, whereas "Dr. Strangelove" was a broad satire.
There are 2 versions of "Fail-Safe". The original stars Henry Fonda, Walter Matthau, Fritz Weaver, Frank Overton, Dan O'Herlihy, Sorrell Booke, and Larry Hagman. The 2000 version has big names, too, but was sort of a pointless remake.
Surprisingly, there are few videos of individual scenes.
The military refused to provide any help whatsoever (and even had stock film houses refuse to help) so every scene of airplanes, or the war room, etc is totally hokey. A clip of a single aircraft taking off was altered in cropping and angle to look like several planes in sequence. The "big board" animation is just bad. A shot of planes "going to afterburner" show them firing missiles instead. A shot of a bomber is a negative image, not positive. Yes, those technical parts are all that bad, but probably most went unnoticed at the time.
Early on, Walter Matthau suggests not recalling the planes.
Later, Frank Overton is trying to help the Russians defend against the bombers. He asks Fritz Weaver to provide some info, but Weaver is starting to crack under pressure. Frank Overton calls up Dom DeLuise (yes) to help.
Near the end, the President (Fonda) is talking to the the Russian chairman. Hagman is the interpreter. ("Jay" is the US ambassador to Russia, in Moscow. The squeal at the end is the sound of his phone melting...). This is a rough clip and continues on but it is unrelated.
My favorite scene - "What do we say to the dead?"
A fan-made trailer is pretty good, and show a bit of most of the characters.