One entry from the era was 1969’s The Monitors. .
Made on a small budget, but with recognized actors (including Susan Oliver 
), but notably filed guerrilla-style for the Chicago exteriors, back when Mayor Daley forbade moviemaking in his city
I don’t know about cult status, but someone at the local off-brand TV station must have liked it because I saw it several times in the 70s
Nah, let him claim his 1940’s level technology.
Oh, and getting back to the topic of the thread, Logan’s Run.
The Invisible Boy (1957) was ahead of its time and darker than one might expect.
I agree with those who note that this genre got started earlier than the 1970-plus-or-minus time frame suggested in the OP.
For example, I recently rewatched Fail Safe from 1964 (the nuclear-crisis thriller that got overshadowed by Dr Strangelove). The premise of the film is that a happenstance collision of technical glitches locks civilization into a path leading to destruction.
The reason I believe this warrants inclusion on the list is that there is explicit dialog in the movie about the risks inherent in technological transformation. There are multiple scenes in which characters talk about how, as computers get faster, more powerful, and more complex, they simultaneously become less comprehensible and controllable; so as people rely more heavily on them, putting more and more decisions and actions directly under computer control, failures become increasingly inevitable, with potentially catastrophic results. This is certainly a reflection of mounting discomfort with the unfolding technology revolution, per the OP.
(Interestingly, while Dr Strangelove has a superficially very similar plot, I wouldn’t put it in the same category; it reorients the story slightly and emphasizes different aspects, making clear that nuclear devastation is a disaster of our own making, precipitated by human foolishness above all else. The technology facilitates the crisis, but it doesn’t cause it as in Fail Safe.)
Silent Running (1972) does NOT entirely fit but its setting and tone is very similar to other 70s sc-fi films.
The technology of the seals in the containment facility fail, though.
I dispute the argument that the “technology gone bad” science fiction sub-genre was unique to the late-'60s and early-'70s because it never really ended. There are many examples in the '80s, like Blade Runner and the first Terminator movie.
It may be a comedy, but Woody Allen’s Sleeper may be the most on-point, given how much of the tech and societal changes indicated (as exaggerated for laughs they might be) has come to pass (or in the case of malignant AI may soon do so), along with the associated dysfunctional totalitarian government.
I never said it was. It’s just that in the late-'60s through the early-'70s they were filmed in the style of the time, which is what the thread is about; not about all eras, which had different styles.
Dark Star is a comedy, but fits with the general style, and has some elements of technology gone bad.
I feel like at that point there’s more of a shift from “technology bad” to “corporations bad”. See also Rollerball, the first Alien, and Running Man.
Dutton’s line “They brought it on themselves,” flat out states that Project Scoop wasn’t thought out. Catch a sample of alien life and what? Bring it to Earth of course! Then, later, discover the BioChem warfare maps that Wildfire’s computer uses and the actual intent of the project seems to become clear.
It’s back to another Crichton line “Your scientists were so preoccupied with whether they could, they didn’t stop to think if they should.”
Silent Running fits that mold too.
At some level they’re all about forces we mere ordinary citizens can’t control:
Tech is not designed to serve us.
Big business is not designed to serve us.
Government is not designed to serve us.
Funny how 50 - 60 years later vs the OP’s time frame this anxiety still feels fresh.