In the 1970s, justices on the Florida Supreme Court were popularly elected. But a number of scandals threatened to topple the court until public outrage led to profound reforms and fundamental changes in the way justices were seated.   One justice abruptly retired after being filmed on a high-roller junket to Las Vegas. Two others tried to fix cases in lower courts on behalf of campaign supporters. A fourth destroyed evidence by shredding his copy of a document into "seventeen equal" strips of paper that he then flushed down a toilet.   As the journalist who wrote most of the stories that exposed these events, Martin Dyckman played a key role in revealing the corruption, favoritism, and cronyism then rampant in the court.   A Most Disorderly Court recounts this dark period in Florida politics, when stunning revelations regularly came to light. He also traces the reform efforts that ultimately led to a constitutional amendment providing for the appointment of all Florida's appellate judges, and emphasizes the absolute importance of confidential sources for journalists.