The microphone can be seen in the first scene, and while they are watching Casablanca, also later when Deverall and his henchmen enter the Ovington Arms hotel room, Donald locks the door and you can see the boom mic.
When Cole and Campbell are walking by the movie theatre, Cole is not wearing gloves. When he shows Campbell the airline ticket, he is wearing one black glove. (This is a reused insert shot from earlier in the film, when Cole was wearing gloves while examining the ticket in the Roslov house.)
After Cole shoots Maynard, Cole is still pointing his gun at him and walking towards him. In the very next shot, Cole is suddenly standing still and holding his gun by the barrel and pointed down to the floor.
When Campbell is shot and the force pushes him out of a window, Cole comes to save the day. After rappelling down and grabbing on to Campbell, a safety strap is shown on their line. In the next shot, you can get a quick shot of a hand pulling onto the line from a nearby window.
When Cole is talking about the dead woman in the autopsy room he says he thinks he's "Russian, most likely Georgian." Russian and Georgian are two distinct nationalities and ethnic groups. The fact that Georgia was at one time part of the Soviet Union does not make Georgians and Russians at all related.
In the first major fight scene against the Russians, the last opponent Jack Cole fights and eventually kicks off the side of the raised cement floor, the same footage of a hand strike to the opponents head is looped and the same strike (camera from behind Cole's left shoulder facing opponent tangentially) is repeated 5 times. A kick from a slightly more distant angle is re-used twice. This is particularly obvious when slowed down and viewed frame by frame, but also apparent at actual speed due to the fact they keep instantaneously 'retreating' and then moving closer to the edge of the floor/ledge area.
When Cole grabs Johnny as he jumps through the school window, there is another window across a gap that is high up, which would mean that the two would go tumbling to the ground, yet Cole and Johnny fly across this huge gap and land through the window on the other side, a physical impossibility.
When Campbell is fighting Donald in Campbell's apartment, Campbell is knocked into his TV, which falls off a short table onto the floor, and sparks are added to the scene with a spark gun nowhere near where the TV fell, and there is no way a TV would emanate sparks from such a short fall, let alone any sparks at all - TVs just don't do that.
During the fight with Campbell and Donald in Campbell's apartment, the stove is jarred off the gas line, and in the short time of the fight, there is no way enough natural gas could be built up to cause the explosion seen. What is more, the next day, the glass that was blown out of the apartment just hours before is back in place.