Some examples of serious problems can be medical problems, landlord problems, legal problems, immigration problems, or something as bad as suicidal tendencies. People are people. Being able to spot serious difficulties isn't hard. They will manifest themselves in the student's demeanor, or the student will just tell you. Often you will be the first person in this country to which the ESL student will bring a real problem.
All serious problems ought to be referred to a specialist.
In most cases, cultural adjustment is the cause for an ESL student's problems. Most ESL programs staff experienced personnel whom you can tap for advice. More experienced conversation leaders and the program's administration no doubt have some valuable experiences to draw on, and they are a great source of information. Remember that ESL students are immersed in an unfamiliar environment, and this can shake a person's values apart. Research has found that adjustment to cultural immersion follows a set of stages.