The one controversy I am remotely familiar with (well, besides the recycling of questions in 1987) is 1997. There is a placeholder for it on QBWiki marked "1997 College Bowl Nationals finals scandal and prize withdrawal", although it could be referring to something else.
Apparently, here's what happened, based on a Usenet post to alt.college.college-bowl: the final was best 2-out-of-3 between Virginia and Harvard. Late in the first game, Harvard led 270-240, but Virginia answered a 10-point tossup and then got a 20-point bonus; "for 10 points each, name the parties that were the first to rule in Israel and India, both of which were voted out of power in 1996." The given answers were Labor (for Israel), called correct, and "INC" (for India, short for Indian National Congress), called incorrect; the "correct" answer was the "Congress party". Harvard now led 270-260 with seconds remaining; the moderator started reading the next 10-point tossup, a Harvard player buzzed in, answered along the lines of, "I have no idea" (costing Harvard 5 points for giving an incorrect answer before the moderator finished reading the question), and time expired, giving Harvard a 265-260 win.
Or did it? Virginia challenged the previous "incorrect" bonus answer, claiming that "Indian National Congress" and "Congress Party" were the same thing. After attempts to find a definitive answer failed (one report said that they even tried asking an Indian student from another team), they decided to ask a substitute 10-point bonus, which Virginia got right, so Virginia won by 5 points (and one of the Virginia players got all "in-your-face" about it). Keep in mind that had Virginia received the 10 points when the question was asked, the game would have been tied, and Harvard would not have buzzed in early in an attempt to run out the clock. In a normal game, this is bad enough, but remember, this was in the National Championship Final.