People mess up "To" and "From" attribution in normal conversation, but I'd say a reasonable person writing a strong attack on someone for major media publication would read a short email carefully, so this mistake is a negligent one. That's enough fault when defaming a private individual, but attacks on public figures require a reckless disregard for the truth, which would be difficult to show here. I think Mann is a public figure on climate issues in the US, although he might have a shot of claiming otherwise in the UK.
An interesting twist on whether the quote actually made by Jones indicates that the speaker is an unfit scientist. I'm sure Jones would disagree. Trying to exclude bad work may have been a mistake, but I don't think it sinks to a level of indicating unfitness. However, Pat Michaels clearly thinks otherwise, and estoppel might prevent him from arguing in court differently from how he argued to the world.
Final aspect of the case is damages. Pat Michaels is a never-important and long-discredited figure in climatology, so his defense would be something like "no one in climatology takes seriously what I have to say, and it doesn't really harm the plaintiff that I misinformed the general public." Cato could point to its own plunging reputation as well (some Cato hack repeated the mistake on the Cato website). These are pretty good defenses.
All in all, it's what lawyers call a colorable, non-frivolous case, but not one I'd bring. Instead, I'd send a letter to Michaels and everyone who published his mistake, telling them that they're not going to get sued but requesting a published correction. Then I'd publish the letter and get some credit for being the better man, even if that's not a difficult achievement in this case.