Axolotl Ratchet is used by the Signal messenger (formerly known as TextSecure) and an enhanced version of OTR in a way to make it suitable for mobile applications, which has the probability to encrypt messages without both parties to have to be online at the same time as described here. The key exchange is happening asynchronously.
Signal also solves a couple of other issues, like out-of-order decryption and preventing metadata to be leaked through cleartexts.
This sounds to me perfect as a replacement for PGP, which is lacking Forward secrecy (PFS) and some other issues.
What problems would have to be thought through, when creating a mail client plugin (like Enigmail for Thunderbird) that uses axolotl encryption instead of PGP?