In the interest of the public good, I will now cite relevant information from the U.S. Bureau of Engraving and Printing:
What is mutilated currency?
Currency notes which are:
NOT CLEARLY more than one-half of the original note and/or,
in such condition that the value is questionable and special examination is required to determine its value.
WHAT IS NOT MUTILATED CURRENCY?
Any badly soiled, dirty, defaced, disintegrated, limp, torn, worn, out currency note that is CLEARLY MORE than one-half of the original note, and does not require special examination to determine its value. These notes should be exchanged through your local bank and processed by the Federal Reserve Bank.
"Mutilated currency" must be processed through the Treasury Department to determine its value, etc. But currency damaged through normal wear and tear retains its full value. So the next time you get hassled at the toll plaza, don't worry. Now you know. And knowing is half the battle.