When Carter pushes the plunger to blow up the base of the tower, the base can be seen having four legs. The shots of the tower that falls down show a three-sided tower. Also, Carter blows the base of the tower first, then the top. If the base were blown first, the tower would be falling when the top was blown. The tower was was seen to be still upright when the top was blown.
Kinchloe's camera is a Pentax, not invented for at least another fifteen years.
Right after Newkirk opens the safe, he brags about his "marvelous fingers." Not only do his lips not match the words, the audio quality dramatically changes from the boom mic to a studio mic.
Carter is not married. In a brief conversation with Hogan about children, Carter confirms this by replying, "I'm not even married." Yet, at the small party in Klink's quarters, he is clearly wearing a wedding ring.