What is the difference between a multiclass problem and a multilabel problem?
I suspect the difference is that in multi-class problems the classes are mutually exclusive, whereas for multi-label problems each label represents a different classification task, but the tasks are somehow related (so there is a benefit in tackling them together rather than separately).  For example, in the famous leptograspus crabs dataset there are examples of males and females of two colour forms of crab.  You could approach this as a multi-class problem with four classes (male-blue, female-blue, male-orange, female-orange) or as a multi-label problem, where one label would be male/female and the other blue/orange.  Essentially in multi-label problems a pattern can belong to more than one class.