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REVIEWS IN BRIEF *As Thousands Cheer: The Life of Irving Berlin Laurence Bergreen (Viking, $24.95) A colorful history of our greatest popular art-the music that emerged out of the ethnic and social commotion of 20th- century America-as well as a vivid biography of its foremost exponent. A
*Behind the Mask: My Double Life in Baseball Dave Pallone with Alan Steinberg (Viking, $18.95) There's some good baseball writing here, but not enough of it-Pallone is too busy creating a second career for himself as a martyr and gay-rights spokesman. C
*The Burden of Proof Scott Turow (Farrar, Straus & Giroux, $22.95) Although The Burden of Proof lacks the sure re thriller devices that helped make Presumed Innocent such a commanding piece of storytelling, readers who persevere will be rewarded. B
*The Burning Season Andrew Revkin (Houghton Mifflin, $19.95) The story of Chico Mendes and his efforts to prevent the destruction of the Amazon rain forest. B+
*Children of the Dragon: The Story of Tiananmen Square (Collier, $19.95) A handsome collection of photographs, speeches, and newspaper accounts documenting last year's ill-fated democracy movement in China. B+
*Coyote Waits Tony Hillerman (Harper & Row, $19.95) The 11th tale in Hillerman's series about the Navajo Tribal Police is sturdy work from an incorruptible craftsman. A-
*Crosstown Traffic: Jimi Hendrix and the Rock 'n' Roll Revolution Charles Shaar Murray (St. Martin's, $18.95) The best book yet on Hendrix-and also a sweeping historical discussion of soul, jazz, the blues, and the impact of electronic technology on pop music. A
*God's Coach Skip Bayless (Simon & Schuster, $19.95) Persuasive as long as it sticks to football, Bayless' book is marred by his haphazard organization and his religious prating. C-
*The Innocent Ian McEwan (Doubleday, $18.95) Far more than an intelligent thriller, The Innocent is also a haunting black comedy charged with psychological complexity, sex, and suspense. A
*Jazz Singing: America's Great Voices From Bessie Smith to Bebop and Beyond Will Friedwald (Scribner's, $29.95) The author's quirks aside, this is quite simply the best available guide to the art of jazz singing. A-
*Language Maven Strikes Again William Safire (Doubleday, $24.95) The sixth collection of Safire's pun- mongering ''On Language'' columns. B
*Saratoga Hexameter Stephen Dobyns (Viking, $16.95) A charming small-town mystery-comedy. B+
*Stardust Robert Parker (Putnam, $18.95) A new episode for Spenser, mysterydom's most self-satis ed shamus. B-
*Too Good to Be True: The Outlandish Story of Wedtech James Traub (Doubleday, $21.95) As Traub deftly shows us, this is a story not about venality but about human frailty. A
ALSO NOTED *Etchings in an Hourglass Kate Simon (Harper & Row, $19.95) The final memoir from Simon (Bronx Primitive, A Wider World), who died earlier this year.
*French Country Kitchen: An Evocation of the Food, People, and Countryside of Southern France Geraldene Holt (Fireside, paperback, $9.95) A cookbook and a memoir brimming with the colors and flavors of Provence-with chapter titles like ''The Pig,'' ''The Olive,'' and ''The Chestnut, Almond, and Walnut.''
*I Love Myself When I Am Laughing And Then Again When I Am Looking Mean and Impressive Zora Neale Hurston (The Feminist Press, paperback, $10.95) An autobiography- sometimes candid, sometimes creatively misleading, always fascinating-of one of America's greatest writers.
*Juke Joint Photographs by Birney Imes (University Press of Mississippi, $39.95) The juke joints of the Mississippi delta. With an introduc-tory essay by Richard Ford.
*The Modern Horror Film John McCarty (Citadel Press, paperback, $15.95) Fifty classics, from The Curse of Frankenstein to The Lair of the White Worm.
*Rough Justice: Days and Nights of a Young D.A. David Heilbroner (Pantheon, $19.95) The vividly drawn experiences of a young Manhattan prosecutor.
*Under a Crescent Moon Daniel De Souza (Serpent's Tail, paperback, $10.95) An Englishman's account of 12 years in a Turkish prison.
