I had 2 main fridge-logic issues which made it very difficult for me to suspend disbelief and limited my enjoyment of the film:
First: Colossus' is only able to implement its plan because the US, and US-aligned nuclear powers, agree to subordinate their entire nuclear arsenals to Colossus' full-authority defence control, with no means of overriding it; and with its computing hardware sealed in an impenetrable fortress (no maintenance access?).
Second: Colossus' plan - and its ultimate actions - assume everyone else on earth is a nuclear-disarmed-rational-actor, all solely interested in not-dying-at-Colossus's-hand - which is an unworkable assumption.
Unfortunately, the story is driven by these 2 points - without either then the film's story would just be yet-another-cliché-movie where the plucky humans beat the advanced AI overlord, the end.
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I still like _Colossus_ because it's "different" to all the other 20th century films with an AI character (c.f. tripe like Will Smith's _I, Robot_ or the Matrix sequels).