At 14:15 into the movie, Colossus displays its first message. The President turns to look at the small monitor, and the display reads "WARN HERE IS ANOTHER SYSTEM". On the big ceiling monitor however it reads "WARN THERE IS ANOTHER SYSTEM", the correct message.
Just after the television transmission during the press conference announcing the activation of Colossus, Professor Forbin calls the CPO and Blake answers the "phone". When he goes to get the phone, some of the pool cues behind him are misplaced in the on-wall rack. A moment later, when everyone else comes over to say hello to Forbin, they are all properly stored.
When Colossus is learning math, Harrison is standing across from Forbin. He is asked to get a printout. When he comes back to Forbin he stands next to him, yet there is a quick shot of him standing across from Forbin and then in the next shot he is standing next to Forbin.
Missile targets are uploaded via software, not with a change of hardware as seen in the film. Colossus could have simply uploaded that data directly.
Forbin's undergarment is visible when he says to Colossus "naked as the day I was born."
When the equations are scrolling past when Colossus and Guardian are "talking" to each other, you can see that they do not actually get ever more complex as the dialogue suggests. Instead, they repeat the same sequence of calculus and trig identities on a repeating loop.
The fascinating and imaginative opening scene in which Dr. Forbin activates Colossus, all the overhead lights come on, punch tape is seen running, displays are on: all of which is for human interface and use. Yet, Dr. Forbin will be the last person to ever be inside Colossus. All of those things should have been turned off as Colossus would have no need for them.
When Missile Commander explains the American and Russian disabling of nuclear warheads in the situation room, he uses a pointer to indicate areas on the map. But when he says, "...and are now working in the Ukraine, in this area," he's putting down the pointer, and has his back to the map.
At about 55 minutes the sound heard from the Alouette II helicopter is that of a piston engine helicopter with a 2-bladed main rotor, but the Alouette II has a jet turbine engine and 3-bladed main rotor which sound completely different.
The first helicopter seen (landing at the Colossus control center) is a 1964 Hughes 300 (269) N9402F s/n: 124-0147. These have a 3-bladed main rotor, but the sound was that of a 2-bladed rotor like the Bell 47G used at the missile silo site.
When the helicopter lands on Isla Tiberina Roma in Rome, Italy, and the door opens, reflections of set lighting can briefly be seen on the Plexiglas window panels.