Mark Dominus on The Universe of Discourse has (fully) explored all the anagrams in Webster’s Second International dictionary.
The longest pair (cholecystoduodenostomy and duodenocholecystostomy) isn’t necessarily the most interesting, as both words are made up of three units (cholecysto, duodeno, stomy) in different orders.
So he came up with a way of scoring pairs based on the degree of rearrangement required:
This gave me the idea to score a pair of anagrams according to how many chunks one had to be cut into in order to rearrange it to make the other one. On this plan, the “cholecystoduodenostomy / duodenocholecystostomy” pair would score 3, just barely above the minimum possible score of 2. Something even a tiny bit more interesting, say “abler / blare” would score higher, in this case 4. Even if this strategy didn’t lead me directly to the most interesting anagrams, it would be a big step in the right direction, allowing me to eliminate the least interesting.
From this algorithm, the most interesting anagram pair is 15 letters long, with only two letters that stay next to each other. Go see what it is.