This article discusses several erroneous claims which appear in textbooks on numerical methods and computational physics. These are not typos or mistakes an individual author has made, but widespread misconceptions. In an attempt to stop these issues from further propagating, we discuss them here, along with some background comments. In each case, we also provide a correction, which is aimed at summarizing material that is known to experts but is frequently mishandled in the introductory literature. To make the mistakes and corrections easy to understand, we bring up specific examples drawn from elementary physics and math. We also take this opportunity to provide pointers to the specialist literature for readers who wish to delve into a given topic in more detail.
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