Q: Are there any non-palindromic words (or meaningful expressions) such that at least one of their anagrams is a palindrome?
A: When working with palindromes it is better to start from the end and work to the beginning (pun intended). In other words, it is easier to find the palindromes in English first and then check if they have anagrams. I found one pair just by thinking about the 3-letter palindromes (dad-add). With a little bit of programming few other pairs can be found: deified-edified, refer-freer, repaper-prepare.