This might be lower hanging fruit than you intended, as the "Real world attack vector" may not be very useful to attack with, as only the AT&T TSD-3600-E was the device to have been known to have implemented this for this, and most other devices appeared to have only be bought by the United States Department of Justice. This said, it might help elaborate on @Kevin's comment on how side-channels are more common to be attack vectors for said algorithms, given the most well known reason it's no longer in use.
The Clipper Chip, and the Law Enforcement Access Field (LEAF)
The LEAF was intended as a way to allow the government to read information necessary to be able to determine the encryption key, and be able to decrypt the message when they had a warrant to do so.
This had 2 major problems later discovered:
1.) Matt Blaze, in 1994, discovered that it was possible to use the fact that the LEAF system requires a 16-bit hash for an encryption key to verify that it was a valid message to encrypt (Such that it could be decrypted), it was possible to brute force for ~30-50 minutes a new 16-bit checksum for a different encryption key than the one used to encrypt the message, effectively bypassing the "Decryptable if necessary" step.
2.) Yair Frankel and Moti Yung in 1995 discovered that it was possible to use one LEAF capable device to generate validation attached for messages encrypted on another device, thus bypassing the "Decryptable if necessary" step in real time.
Ultimately, these issues are what most likely lead to the disuse of this method, with the U.S. government being the most notable largest customer of the AT&T TSD-3600-E. I'm unaware of how many of these were actually used as a result, since reportedly most of the boxes were left unopened. Which leaves us with concerning the actual Skipjack cipher.
This was the encryption that, as I understand, was used by the Clipper Chip such that, without that valid LEAF from the hashes above, would be secured against someone decrypting what was in the message.
This is harder to proof that it was proven secure, given that originally, it was classified, but...Academic researchers were brought in to evaluate Skipjack, and found that "Thus, there is no significant risk that SKIPJACK will be broken by exhaustive search in the next 30-40 years."
June 25, 1998, when Skipjack was declassified, Eli Biham and Adi Shamir had discovered that when Skipjack is reduced to 16 instead of 32 rounds, it was breakable with an attack vector discovered at that time. Later in 1999, with Alex Biryukov, they were able to extend it to 31 of 32 rounds.
Apparently, as of 2009, a full breakthrough of all 32 rounds had not been fully broken, but these appear to indicate that the original proof may have been wrong, given that it appears that the first 31 rounds of 32-round Skipjack relied primarily on the classification of the algorithm at the time.
As @Kevin said in his comment to the question above, primarily side-channels would be the way to break it - and in this case, the Clipper Chip and its LEAF protocol itself proved to be the weaker link - breaking the protocol that would have been used to decrypt the underlying encrypted messages when warranted.