Some of these might be debatable because the MyThes thesaurus I used as a source is rather inclusive.
I filtered a ton of false positives, here is a sampling of them:
technical terms with trivial differences (e.g. alexandrian senna vs senna alexandrina)
loan words with multiple acceptable spellings (e.g. harakiri vs harikari, schtik vs shtick)
minor spelling differences and errors (e.g. despoilation vs despoliation)
phrases pluralized inconsistently (e.g. herb roberts vs herbs robert)
AmE vs BE differences (e.g. theatre vs theater)
the same stems in the opposite order (e.g. lookout vs outlook)
For my source code and full results, including an annotated list of excluded words, see this git repository.
From a computer science perspective, this is not a particularly interesting problem. Finding anagrams is quick and easy, so the only limiting factoring is reading through the whole thesaurus, which is slow simply because of the number of words included. In general, no problem can be solved faster than the time it takes to read the input.