Filing a tax return by yourself?

I have a question - my husband and I filed our taxes jointly, but instead of going through a company to do it, we did it ourselves and mailed it in. It was a simple tax return, no deductions or itemization or anything. Well, my worry is that what if we made an error or something on it (obviously not on purpose), what would happen then? Would they send it back for us to correct or would they correct it themselves? Would we have to pay any penalties and fines on it? I'm just really worried since this is our first time ever doing it like this - we did owe taxes and we sent a money-order in along with the tax return. Thanks so much! Oh, I forgot to mention: we did the federal tax using TurboTax - we printed it out and mailed it, but we did the state tax return ourselves with no help.