In some languages, palindromes are fairly easy to construct.
However, to some extent this is a result of the writing system – for instance, in English ‘hs’ is almost nonexistent, which means that ‘sh’ cannot be used in palindromes; if English started using ‘š’ instead of ‘sh’, it would immediately allow for more palindromes.
On the other hand, if we look at phonetic palindromes, any such bias created by the writing system should disappear. By ‘phonetic palindrome’, I mean an utterance that sounds more or less the same if played backwards.
Phonetic palindromes are definitely possible. In English, for instance “Say ‘Mum, yes!'” [?s?j ?m?m ?j?s] (writing [?j] instead of the usual [e?]), and in Danish, “Dannie gik i nat” /?d?æni ?g?ig? i ?næd?/.
However, I didn’t find it very easy to construct these, and I wonder whether there are languages that allow you to construct phonetic palindromes of a reasonable length?
I can see some potential issues that will limit the ease of construction in certain languages. For instance, in Danish and most varieties of English, /p t k/ are aspirated, which means that they are phonetically [p? t? k?]; when these are reversed, they result in [hp ht hk], and these sequences do not occur in Danish and English.