There is no mathematical error in TurboTax, and it does not use the blended tax rate to calculate your tax. The blended tax rate is just informational, to give you an idea of the overall percentage of tax that you are paying. The blended tax rate is derived from the amount of your tax. The amount of tax is not derived from the blended tax rate.
You used the Tax Rate Schedules to calculate your tax. You overlooked the "Caution" at the top of the Tax Rate Schedules, which says the following (emphasis added).
"The Tax Rate Schedules are shown so you can see the tax rate that applies to all levels of taxable income. Don't use them to figure your tax. Instead, see the instructions for line 16 [of Form 1040]."
The instructions for line 16 tell you that "If your taxable income is less than $100,000, you must use the Tax Table . . . to figure your tax." That's what TurboTax does, and if you use the Tax Table you will get the same result. The Tax Table is based on $50 increments of taxable income. All incomes in a particular $50 range have the same amount of tax, so there is a variance of a few dollars from an exact percentage.
