A common cause of the tax not appearing to be right is because the taxpayer has qualified dividends or capital gains (or both). In this case, the tax calculation is shown on a worksheet called "Qualified Dividends and Capital gains Tax Worksheet" (or something close to that).
The reason for this is that qualified dividends and capital gains are taxed at a lower rate than ordinary income. This means that when you look at the Tax Table for this taxable income, you don't see the same result on the tax return. There are some other situations in which tax is calculated using something other than the Tax Table, but qualified dividends and capital gains are the most common reason.