I am not sure I have faced many difficulties needing resolving, but have made use of my knowledge of cultural differences to stimulate discussion in my classes.  I am English and moved to France seven and a half years ago.  I work voluntarily with adults, mainly retired, who are learning English for fun and for use when travelling abroad. 

The first cultural mistake I made was at the very beginning of my very first session when I called them all by the first names which they had written to register.  It would have been expected that I use the more formal Monsieur or Madame until I knew them better.  By the times I'd realised this - weeks or months later, I could only point out I had made a cultural mistake!

Other mistakes have arisen from false friends in vocabulary. I asked them about art galleries and they answered exclusively about shops that sold paintings, not about the Musée des Beaux Arts.  This was rectified as I realised we were not discussing the same thing.

I can't remember when they felt they knew me well enough to kiss me on each cheek on arrival.  In my class a latecomer does not disrupt the class by kissing the other dozen members as he arrives - probably because to begin with I never stoppped what I was doing to give anyone the chance to do this.  The others no doubt realised that British culture doesn't allow for this. 

With my beginners, I teach the vocabulary for a typical British breakfast very early on, as this is what they will encounter in hotels and their need for English is almost exclusively as tourists.  This obviously contrasts with their country's typical breakfast.

I have used cultural and other differences as bases for lessons at various levels as this is of great interest to my students.  Though I anticipated cricket and tea -drinking, I wasn't expecting The Queen Mother's hats to figure high on the list.  I have asked what they think is typical, on another occasion, what they think is different between the two countries.  They are unaware that supermarket queues and after sales service are bad in France - or that their food really is an art form and not only very good, but reasonably priced compared to Britain.

Another point of interest - and also a cause of surprise is the number of French words we use regularly in English.  They know they have many English words and that the Académie Française objects, but don't realise that we use many French words, but we don't mind. 

As French handwriting is different from British handwriting, more looped with extra upstrokes before letters like n, I sometimes handwrite them a postcard and photocopy it to give them practice in reading foreign writing.  I find theirs difficult to read unless the style is very basic and carefully written!

Hope this is useful, Monica.  If I can be of further help, please contact me.