Exploitable mathematical structure arising purely from the concept of an iterated cipher is probably what Nick meant there by "an actual mathematical break". SHACAL-2 is also an iterated cipher with a relatively simple round structure.
Pretty much all block ciphers (and therefore their derivative constructions) are iterated.
The SHACAL-2 permutation though is much more mathematically unstructured than AES. It's an augmented ARX unbalanced Feistel design (w/ additional non-linearities). Hard to imagine you could reconstruct any usable mathematical structure in that mess. It also has a strong key schedule which is not vulnerable to related-key attacks (AES is) which is by design due to its hashing application. 512-bit key space too which allows for easy nonce integration.
Most block ciphers iterate the same round function, but this regularity is destroyed by using distinct round keys in each round.
The only vulnerabilities of the iterated construction appear when a weak method is used for generating the round keys from the cipher key (i.e. when the so-called key schedule is weak), so that there are predictable relationships between the round keys.
There exists an alternative (and equivalent) construction for a block cipher, when the same key is introduced in all rounds, but in this case all the round functions must be different from each other (instead of iterating the same function).
Ironically, the reason SHA2 isn't reachable by the attacks that broke SHA1 is the simplicity of the SHA1 message schedule, which was also by design due to its hashing application.
SHA1 has a sloppy key/msg schedule. They could have just done a random permutation of words and been safe - it would have even been cheaper than what the ended up doing. Such as what BLAKE does.
