I have no federal penalty due, but I do for the state. This is due to (1) federal but not state withholding for SSA benefits, and (2) large capital gain in December.
TurboTax says I don't owe a penalty and doesn't give me a way to specify the date of various income items to correct this.
And....you say one of the problems is that there was nothing withheld from your Social Security for state tax. Do you live in one of the states that taxes Social Security? Only a few states tax Social Security benefits.
There are 11 states that tax Social Security—Colorado, Connecticut, Kansas, Minnesota, Missouri, Montana, Nebraska, New Mexico, Rhode Island, Utah, and Vermont
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The issue isn't that the Social Security is taxed. The bulk of the tax is on investment income at the end of the year. But the federal withholding on the SSA income is spread throughout the year, and is enough to avoid a penalty.