This one is easy: Change your address with the IRS when you move. If the IRS thinks your tax return is wrong, they send a letter telling you what they think is wrong and giving you a chance to fix it or argue it. If you ignore the letter (which they hate) they send another where you are no longer arguing and they just want money. Ignore that one, and they start sending more threatening letters and start talking about liens and going after your paycheck or bank account. If they have the wrong address, you might as well be ignoring them.
Filing a tax return changes your address automatically, so if you move just before filing, you are already okay. If you file just before moving, feel free to use the new address on your return. Otherwise, go to HERE and fill out Form 8822.