Collecting a series of stories mostly written for magazines in the 1940s, I liked this book better the first time I read it. The first story is best, and the second is good, though the authors ran out of either time or energy and finished in a rush. The last story in the series is weak, and so full of stereotype that it verges on unintentional and unpleasant parody.
In all the stories, the 'science' is no more than a few mumbled buzzwords that provide an excuse for a set of Connecticut Yankee-type episodes, though not as well thought out as Twain's effort. The stories are mostly fun, but they haven't aged very well. If you remember liking these, stick with that memory. If you haven't read them, these won't hurt, but some of De Camp's solo work might provide a better payoff.
By the way - the first two stories in the book were published as The Incomplete Enchanter, thus the title here of The Complete Enchanter. But there are in fact two more stories, in another book, sometimes called The Enchanter Completed. Confusing, but basically there are five long stories in the set. (Which one publisher gathered as The Compleat Enchanter Completed.)