I personally prefer asking the non-Muslims upfront, with their limited knowledge, whether right or wrong, from which ever source it may be, what they feel is wrong in Islam. I encourage them to be very frank and open and convince them that I can take criticism about Islam.
In current situation you will find that the questions that non-Muslims have can be assemble into few comman questions.
Whenever you ask a non-Muslim, “what do you feel is wrong in Islam?”, he poses five or six questions, and these questions invariably fall among the few most common questions.
The most common questions about Islam can be answered with reason and logic. A majority of non-Muslims can be convinced with these answers. If a Muslim memorizes or simply remembers these answers, Inshallah he will be successful, if not in convincing non-Muslims about the complete truth of Islam, then at least in removing misconceptions about Islam and neutralizing the negative thinking about Islam and Muslims that the non-Muslims have.
A very few non-Muslims may have counter arguments to these replies, for which further information may be required.