TOM BRADLEY--THE IMPOSSIBLE DREAM by J. Gregory Payne & E. Scott Ratzan (Roundtable: $18.95; 368 pp., illustrated). The authors do not miss a virtue as they tell the story of Los Angeles Mayor Tom Bradley's climb from his parents' cotton sharecropper's cabin in Calvert, Tex., to the city mayoral mansion in Hancock Park and his present role as Democratic nominee for governor of California. Unfortunately, they do not catch many faults, either. As a result, the mayor emerges saintlike from an overly admiring book. But J. Gregory Payne and E. Scott Ratzan have done the best job so far of researching the mayor's life and uncovered material that has never been published before. A chapter on "Public Success and Private Sorrow" provides a revealing and moving account of daughter Phylis' drug addiction. And Bradley's 1982 loss to Gov. George Deukmejian is more understandable after their story of infighting among the staff that year. Too bad that the authors took such an uncritical look at an important American political figure, glossing over mistakes, and not examining the negative side of such decisions as the Bradley alliance with the real estate industry, which is bringing congestion--as well as construction jobs--to the city.