While I have a basic understanding about one-time pads and how they work, I realize that there must be something wrong with this idea but I don't know enough to figure out what.
There are vast amounts of publicly available documents on the Internet. Why can't Alice and Bob agree that they will use the text of the first article posted on Slashdot after noon Central Standard Time each day that they have a message to send as their one time pad?
That isn't a One-Time Pad. In OTP the pad is secret; in the scenario you just described, the content of the "pad" is public. The encryption key is thus not the pad itself, but rather just the identification of the pad ("1st article on Slashdot after noon CST"). Putting aside the fact that an article has relatively low entropy per character, someone with access to just one cyphertext could conceivably test it against a large database of likely public documents and identify the pad simply by looking for a document which decrypts the cyphertext into something intelligible. Given a couple of cyphertexts they could derive the rule you use to select your "pads". In a true OTP setup there is no way to determine whether a given pad decrypts the cyphertext since every possible plaintext has an equally plausible random pad, and even knowing both cyphertext and plaintext for the same message gets you no closer to being able to decode future messages.