Notice that "issues" is plural. Shelton is probably being precise here and there's more than one reason or more than one issue of "integrity and character".
Perhaps one of the issues was the one in Bob Novak's latest column at:
http://www.suntimes.com/output/novak/cst-edt-novak22.html
Clark was a three-star lieutenant general who directed strategic plans and policy for the Joint Chiefs of Staff. On Aug. 26, 1994, in the northern Bosnian city of Banja Luka, he met and exchanged gifts with the notorious Bosnian Serb commander and indicted war criminal, Gen. Ratko Mladic. The meeting took place against the State Department's wishes, and may have contributed to Clark's failure to be promoted until political pressure intervened. The shocking photo of Mladic and Clark wearing each other's military caps was distributed throughout Europe.
"In fact, he tried to play the hawkish Blair off against the distracted Clinton during NATO's Kosovo campaign. Some NATO air commanders, especially the American ones, blamed Clark for compromising with NATO's political leaders too much on targets early in the war, thus lengthening the campaign. After weeks of trying to corner and back channel Clinton and the Joint Chiefs into launching a ground war, Clark was virtually quarantined from the war council. "I rue the day I made him SACEUR," Defense Secretary Bill Cohen is reported to have said.
In an unmistakable sign of his anger with Clark's style, Joint Chiefs Chairman Henry Shelton didn't even bother attending Clark's formal retirement ceremonies. Shelton wasn't alone: Several other chiefs were AWOL as the Pentagon saluted General Clark for his abbreviated tenure.
— Alan W. Dowd is a research fellow and director of the Indianapolis office of the Hudson Institute.