Of course they are numbered, just like any $1 bill. They are not registered as far as I can tell; they are bearer bonds (just like a $1 bill).
Now say you have several trillion dollars outstanding to many people who are not quite your friends, nor very interested in rummaging through their books to help you, revealing their hands in a very high-stakes game. Then some other government turns up a ridiculous amount of bonds designed to be anonymous (just like a... you get the picture). Also, a third government has some claim because it crossed her border.
That is a classic "international incident". It will take some time to resolve. Lots of favors will be traded. Joe Public may never know the details.
"Bonds that are lost, stolen, mutilated or destroyed, can be replaced free of charge as long as it can be established by the Bureau of the Public Debt that the bonds are still outstanding. To assure that bonds can be traced, owners should keep records of bond serial numbers, issue dates, [etc.]"
I think we can do better than appeal to a fictional dramatization as authority.
The difference between an unregistered bearer bond and other types of bonds is that the bearer bond is not registered to a particular individual, but instead guarantees payment for the bearer of the bond. Other bonds are registered with the social security number of the bond recipient.
However all bonds have serial numbers, regardless of whether they are registered. This is how the government verifies the validity of the outstanding debt guaranteed by the bond. Otherwise, what is to stop some counterfeiter from manufacturing fake bonds and claiming them?