score:7
Zinn's book is not so much a history as a collection of essays in chronological order.
His book projects a modern left-wing view of events which often veers into distorted depictions that the original participants would have found barely recognizable. His facts are excellent and correct, but he omits key information and ends up portraying things in a false light. For example, when writing of the expansion of the railroads, he describes them as conducting "battles" with Indians whose "territory they had invaded". While battles certainly did occur, they were rarities. Nearly always the railroads made financial arrangements with the Indians, essentially paying protection money, to win their favor. Zinn makes no mention of this, even though this was the standard thing that happened.
Rather than use a different text book, I would recommend referring to original sources. In prior years it was hard to do this, but now with Google Books, you can instantly read contemporary accounts of history that will give you a much deeper insight into the past than any history book will. Autobiographies are especially useful and interesting in my experience. For example, one good autobiography is that of Calvin Coolidge. It is very short, but paints an indelible picture of life in turn-of-the-century Vermont.
Other good sources are "county histories" such as the History of Washington County from Its First Settlement to the Present Time by Alfred Creigh (1871). This tells the story of the place my ancestors are from. If you find the county history from your ancestors' place of origin, not only will you learn history, it will have a personal importance for you.