mutual differences

It is a rather awkward expression. It is common enough, however, that a native speaker (of the American language at least) would likely understand. It means those things about which the couple commonly argue. Technically, it is an illogical construction--but then, many expressions in any language don't necessarily sound logical, but are understood by the native speakers.

Probably the most prominent example of the "abuse" of the term "mutual" is the expression "our mutual friend." That means someone who is a friend of both the speaker and the person he or she is addressing. Grammarians wax angry over that usage, and say that it is not a logical usage of the word mutual. Nevertheless, Charles Dickens used Our Mutual Friend as the title of the last novel he completed before his death. You can read Our Mutual Friend by clicking here. (The last novel he was writing when he died was The Mystery of Edwin Drood--but he died before completing the novel.)

Thanks for your reply, Setanta!
When I was a child our TV was broadcasting the serial Teleplay Our Mutual Friend. I couldn't quite understand the content then really. And my mother has been quite enjoying reading Dickens's novels, the translated version of course. :wink: