NEAL PEIRCE has written a number of scholarly books on the 50 states, but in this one, done with his colleague at the National Journal, Jerry Hagstrom, he kindly leaves behind much of the scholarly baggage and takes us on what, by comparison, could be considered a pleasure tour. The authors have attempted, with abundant success, to create what they call "a modern-day sequel to John Gunther's Inside U.S.A., researched during World War II and published in 1947."

The Book of America is easy to get through, but it stirs some queasy feelings about the future of this country. Peirce and Hagstrom found some degree of mismanagement, despoliation, and decay almost everywhere. What does it say about Americans that one of our most influential senators represents a state whose major industries are mob- allied gambling, quickie divorces, and prostitution? Is it a national or only a regional character defect that prompts rich Texas to run a prison system with one doctor per 17,000 prisoners? Why do we insult ourselves by giving so much importance to our least common denominator, the presidential primary in New Hampshire, a state whose sleazy, sloppy government "permitted America's most bizarre and self- centered political environment to flourish"?

Cities of the South and West, having apparently learned nothing but arrogance from watching Eastern cities go to pot, are blithely employing even faster methods of suicide. Houston, the only major U.S. city without zoning laws, has been properly described, say Peirce and Hagstrom, as "27 significant buildings surrounded by trivia." Atlanta "has never developed a master plan . . . and it has shown pitifully small regard for historic preservation." Denver has developed such an awful traffic problem that its air pollution is "second only to Los Angeles." Phoenix, which in the past three decades has expanded in area from 17 square miles to 330 square miles, "has failed to retain any of the special Southwestern flavor of its birth." And so forth.

Non-urban areas are being subjected to special plunder. For example, in Arizona nature-loving Americans are stripping the desert of cacti--to decorate patios, I suppose--and our most notorious vandals, the Army Corps of Engineers, "have removed huge swatches of water-consuming mesquite shrubs and salt cedar trees" along the rivers so that retirees from Ohio can have more water for their swimming pools.

To help keep the Mafia alive and well in Nevada, the federal government has not only subsidized the water supplies for Las Vegas and Reno but has allowed developers to ruin lakes and rivers and vast stretches of what were once wildlife habitats. What is happening in Nevada is, to Peirce and Hagstrom, "the most appalling assault on God-given natural beauty on the American continent."

And just about everywhere Peirce and Hagstrom traveled, they found some degree of racial and/or economic bullying. An ironic twist surfaced in San Francisco, where a homosexual real estate speculator in a ghetto said, "Why the hell should this gem of a city be given over to welfare blacks. Put them in Idaho, or at least in Oakland." In America, it seems, the sign of success is when discriminatees can afford to become discriminators.

But I'm making the book sound too negative. For the most part, Peirce and Hagstrom are upbeat. Or at least they try very hard to be, sometimes with grotesquely unpromising material. They acknowledge, for instance, that Camden, New Jersey, is "physically repulsive, an unordered melange of ancient boxlike factories, . . . dingy row houses, a blighted waterfront, and barren, empty fields," but, gritting their teeth with effort, they complete their report on it by insisting that they have heard "reports" of "gentrification."

The solid scholarship and endless legwork that obviously went into The Book of America are impressive indeed. Still, I would timidly quarrel with a few of the things they say about some of the states with which I have a passing acquaintance. They have little praise for West Virginia, which is understandable; but I think they should have jumped at the chance to give due credit to the Charleston Gazette, one of the great boondocks newspapers. They pass it off in one sentence merely "a progressive and sometimes crusading force" in Charleston itself. In fact, the Gazette's constant, loud, and radical crusading has sent several state officials to jail, and with 50 percent of its circulation outside Charleston, its influence is statewide and powerful.

Of Florida--which is where I sit as I write this review -- they make several justified complaints about the tax system and several that are unjustified. For example, they say that "there is a homestead property exemption that makes it extremely difficult to raise taxes in poorer sections of the state." Thanks to that $25,000 homestead exemption, a lot of low-income homeowners don't have to pay any property tax. Is that bad?

With the coming of the Cubans, Miami was Latinized and with its Latinization came drugs and with drugs came a bountiful crime rate (as well as great prosperity to the many Miami banks that launder drug millions). But, looking to the bright side of the Cuban invasion, Peirce and Hagstrom quote with approval Mayor Ferre's appraisal that "had it not been for the Cubans moving in here, Miami would be a limp, sick, anemic place." Nonsense. To say that the most important city in one of the fastest growing states depended on the Cuban influx for its health is about as silly as to suggest that had it not been for the flood of illegal Mexicans into Los Angeles, that city would also be limp, sick, and anemic.

Florida's capital, Tallahassee, is a nice little town, but until Peirce and Hagstrom said so, I had never heard anyone claim that it was "renowned for its parklike hills lined with giant oaks and antebellum mansions." Oaks there are aplenty; but those who know Tallahassee's history best tell me that it has only three antebellum mansions and one of them is sorely in need of repair.

They see "cosmopolitanism" in Forida's Panhandle. Well, yes, some stretches--those that aren't rural backwardness-- are about as cosmopolitan as a plastic motel room.

But enough quibbling. Aside from its other virtues, The Book of America is fun. Its survey of history, geography, politics and foolishness is prolific with incidental information--the kind of trivia that makes America go 'round and that will enable you to drive your family and friends batty with question games.

1. In what state was an attorney general recently elected on the promise that he would "fry" murderers "till their eyes pop out and smoke comes out their ears"?

2. What city has the nation's only Wino Park complete with campsite and extra-wide benches for sleeping?

3. In what U.S. city of 82,000 residents is French the dominant language?

4. Ten percent of the nation's cotton is harvested within 50 miles of what excruciatingly dull city?

5. What state had a high school dropout rate of 42 percent in 1982, compared to 10 percent nationwide?

6. Here's an easy one: What state has a gross product -- $350 billion--greater than those of all nations but the United States and six others?

7. Who denounced Mrs. Martin Luther King as an "outside agitator" for urging Alabama blacks to vote against George Wallace last year?

8. Which state saw its farm employment drop from 46 percent of the work force in 1930 to 3 percent in 1980?

Of all the information Peirce and Hagstrom have supplied, I think I may be most grateful for a bit that came out of Hagstrom's home state, North Dakota: That, I now know, is the birthplace of singer Peggy Lee, born Norma Egstrom.