Jack Bristow leaves the CIA with a bandage on his face, in a scene or two later in the elevator with Sydney the bandage is gone.
The shot of Jack watching Sydney haul up the magnet after the explosion damages the lab and causes the scrambler to drop is repeated from an earlier attempt and shows none of the damage from the explosion.
The failed mission that Cole was on was in 1996. Cole said that the KGB contacted the CIA through various channels to confirm whether or not he was a CIA operative, but the KGB was disbanded in 1991.