SATURDAY JANUARY 21, 1989 by, Michael Kernan At the Peace Park opposite the White House, men and women weregiving out petitions against nuclear weapons. They collect an average of 4,000 names a month, they said. But then, the Anti-Nuclear Vigil has been going on for 8 years and doubtless will be wlth us long after the inauguration. Two reporters approached the truth, seperating the homeless from the peace demonstrators who help them... However, one reporter wins our "Sloppy Journalism Award": COMPARE THE DISTORTION!, By,Sandra G. Boodman 1-20-89 For weeks the residents of LaFayette Park-some alcoholic, others mentally ill, all poor-have listened to the high-pitched whine of power saws as the construction workers erect an impressive blue and white reviewing stand in front of the White House. Some resent the elaborate preperations for a celebration that, at an expected cost of $30 million, will be the most expensive in history. (Bottom Line=$50 million)